Easily Explain or Interpret Meaning of a Derivative in the Context of the Problem @turksvids

turksvids AP Calculus Exam Review!
In this video we talk about how to interpret or explain the meaning of a derivative in the context of the problem in which you found the derivative. In general you want to follow the process of identifying the input of the derivative, identify what the original function tells you, decide if our function is increasing or decreasing, and then find or state the units of the derivative. We do a whole bunch of problems pulled from released AP Calculus Free Response Questions (FRQs). The FRQ parts we look at are: 2007B (3a), 2009B (2b), 2012 (1a), 2013 (1a), 2014 (1b), 2017 (2b), and 2021 (1a).

You will definitely have to do this at some point on the AP Calculus AB or AP Calculus BC exam. This is an idea specifically mentioned in Unit 4 of AP Calculus.

AP Calculus Free Response Questions can be found here:
apcentral.collegeboard.org/courses/ap-calculus-ab/exam/past-exam-questions

updated 3 years ago

Easily Explain or Interpret Meaning of a Derivative in the Context of the Problem

turksvids 2023-04-02 | AP Calculus Exam Review!
In this video we talk about how to interpret or explain the meaning of a derivative in the context of the problem in which you found the derivative. In general you want to follow the process of identifying the input of the derivative, identify what the original function tells you, decide if our function is increasing or decreasing, and then find or state the units of the derivative. We do a whole bunch of problems pulled from released AP Calculus Free Response Questions (FRQs). The FRQ parts we look at are: 2007B (3a), 2009B (2b), 2012 (1a), 2013 (1a), 2014 (1b), 2017 (2b), and 2021 (1a).

You will definitely have to do this at some point on the AP Calculus AB or AP Calculus BC exam. This is an idea specifically mentioned in Unit 4 of AP Calculus.

AP Calculus Free Response Questions can be found here:
apcentral.collegeboard.org/courses/ap-calculus-ab/exam/past-exam-questions

Calc BC Problem Set 05

turksvids 2023-09-20 | Link to problems: drive.google.com/file/d/16wkQCd3EBfReUrtb-9TszUEkHL-VSoME/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZiztQ-9heM-_mQzDI3t85nJy
Link to Calc AB-level Problem Sets: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics: (Descriptions from CB AP Calculus CED)
10.11: Finding Taylor Polynomial Approximations of Functions
2.1: Defining Average and Instantaneous Rates of Change at a Point
7.3: Sketching Slope Fields
6.4: The Fundamental Theorem of Calculus and Accumulation Functions

Full list of problems/CED correlations for all BC problem sets: docs.google.com/spreadsheets/d/1vAk1aGAB19LM8BB4xzpLC7AVt4EKOk8_o9rFfMN23IE/edit?usp=sharing

Any calculator work is done on the TI-Nspire CX II CAS. If I use the solve function and you don’t have a CAS, you can use graphing and intersection points instead.

*AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, any of my videos or work.

Calc BC Problem Set 04

turksvids 2023-09-17 | Link to problems: drive.google.com/file/d/1X5ECmD6IAUMl5te-hRdocYdbvh49LIFD/view?usp=drive_link
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZiztQ-9heM-_mQzDI3t85nJy
Link to Calc AB-level Problem Sets: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics: (Descriptions from CB AP Calculus CED)
2.3: Estimating Derivatives of a Function at a Point
1.16: Working with the Intermediate Value Theorem (IVT)
5.1: Using the Mean Value Theorem
6.10: Integrating Functions Using Long Division and Completing the Square
6.12: Using Linear Partial Fractions
6.11: Integrating Using Integration by Parts

Full list of problems/CED correlations for all BC problem sets: docs.google.com/spreadsheets/d/1vAk1aGAB19LM8BB4xzpLC7AVt4EKOk8_o9rFfMN23IE/edit?usp=sharing

Any calculator work is done on the TI-Nspire CX II CAS. If I use the solve function and you don’t have a CAS, you can use graphing and intersection points instead.

*AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, any of my videos or work.

Calc BC Problem Set 03

turksvids 2023-09-13 | Link to problems: drive.google.com/file/d/1yGDZ8osp2wcsa4Dq9ewBU0VSvxrIW0CT/view?usp=drive_link
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZiztQ-9heM-_mQzDI3t85nJy
Link to Calc AB-level Problem Sets: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics: (Descriptions from CB AP Calculus CED)
6.9: Integration using Substitution
6.11: Integrating Using Integration by Parts
7.7: Finding Particular Solutions Using Initial Conditions and Separation of Variables
8.8: Volumes with Cross Sections: Triangles and Semicircles

Full list of problems/CED correlations for all BC problem sets: docs.google.com/spreadsheets/d/1vAk1aGAB19LM8BB4xzpLC7AVt4EKOk8_o9rFfMN23IE/edit?usp=sharing

Any calculator work is done on the TI-Nspire CX II CAS. If I use the solve function and you don’t have a CAS, you can use graphing and intersection points instead.

*AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, any of my videos or work.

Calc BC Problem Set 02

turksvids 2023-09-10 | Link to problems: drive.google.com/file/d/1WapHYTQF2kg2Qpx1JT3A-mvqjUR7dzXr/view?usp=drive_link
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZiztQ-9heM-_mQzDI3t85nJy
Link to Calc AB-level Problem Sets: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics: (Descriptions from CB AP Calculus CED)
7.7: Finding Particular Solutions Using Initial Conditions and Separation of Variables
6.10: Integrating Functions Using Long Division and Completing the Square
6.11: Integrating Using Integration by Parts

Full list of problems/CED correlations for all BC problem sets: docs.google.com/spreadsheets/d/1vAk1aGAB19LM8BB4xzpLC7AVt4EKOk8_o9rFfMN23IE/edit?usp=sharing

Any calculator work is done on the TI-Nspire CX II CAS. If I use the solve function and you don’t have a CAS, you can use graphing and intersection points instead.

*AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, any of my videos or work.

Scan to Single pdf in Google Classroom

turksvids 2023-09-09 | In this very short video I go over how to scan your work and end up with a single pdf file through Google Classroom. I'm using an iPhone, but I bet the process is similar (or easier) on Android.

Calc BC Problem Set 01

turksvids 2023-09-06 | Link to problems: drive.google.com/file/d/1hrVwOR2Bebnw6OjNx8Rn6XBhrLQvrab-/view?usp=drive_link
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZiztQ-9heM-_mQzDI3t85nJy
Link to Calc AB-level Problem Sets: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics: (Descriptions from CB AP Calculus CED)
6.10: Integrating Functions Using Long Division and Completing the Square
6.12: Using Linear Partial Fractions
8.4: Finding the Area Between Curves Expressed as Functions of x
8.12: Volume with Washer Method: Revolving Around Other Axes

Full list of problems/CED correlations for all BC problem sets: docs.google.com/spreadsheets/d/1vAk1aGAB19LM8BB4xzpLC7AVt4EKOk8_o9rFfMN23IE/edit?usp=sharing

Any calculator work is done on the TI-Nspire CX II CAS. If I use the solve function and you don’t have a CAS, you can use graphing and intersection points instead.

*AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, any of my videos or work.

Find Potential Function, Conservative Vector Field || Multivariable Calculus (Assignment 11, pt 4)

turksvids 2023-06-05 | Assignment 11, part 4.

In this video we either find a potential function for a conservative vector field or show that the field is not conservative (by calculating the curl and showing it is not 0).

These are fully worked out problems with commentary.
0:00 Number 14
1:49 Number 15
3:33 Number 16
5:34 Number 17

This is a common topic in Calculus III, Multivariable Calculus

Greens Theorem Problems || Multivariable Calculus (Assignment 12, pt 3)

turksvids 2023-06-01 | Assignment 12, part 2.

In this video compute a line integral using Green's Theorem to set up the corresponding double integral and then computing its value .

These are fully worked out problems with commentary.
0:00 Number 7
2:11 Number 8
4:13 Number 9
8:36 Number 10

This is a common topic in Calculus III, Multivariable Calculus

Greens Theorem Problems || Multivariable Calculus (Assignment 12, pt 2)

turksvids 2023-05-31 | Assignment 12, part 2.

In this video compute a line integral using Green's Theorem to set up the corresponding double integral and then computing its value .

These are fully worked out problems with commentary.
0:00 Number 3
1:49 Number 4
4:31 Number 5
7:07 Number 6

This is a common topic in Calculus III, Multivariable Calculus

Greens Theorem Problems || Multivariable Calculus (Assignment 12, pt 1)

turksvids 2023-05-30 | Assignment 12, part 1.

In this video compute a line integral directly and then use Green's Theorem to set up the corresponding double integral and then compute .

These are fully worked out problems with commentary.
0:00 Number 1
4:02 Number 2

This is a common topic in Calculus III, Multivariable Calculus

Find Potential Function, Conservative Vector Field || Multivariable Calculus (Assignment 11, pt 3)

turksvids 2023-05-29 | Assignment 11, part 3.

In this video we either find a potential function for a conservative vector field or show that the field is not conservative (by calculating the curl and showing it is not 0).

These are fully worked out problems with commentary.
0:00 Number 7
2:08 Number 8
4:23 Number 9
6:31 Number 10
8:06 Number 11
9:53 Number 12
11:41 Number 13

This is a common topic in Calculus III, Multivariable Calculus

Conservative Vector Field, Fundamental Theorem || Multivariable Calculus (Assignment 11, pt 2)

turksvids 2023-05-28 | Assignment 11, part 2.

In this video we confirm that a vector field is conservative and then use the fundamental theorem to evaluate the line integral.

These are fully worked out problems with commentary.
0:00 Number 3
1:37 Number 4
3:08 Number 5
4:46 Number 6

This is a common topic in Calculus III, Multivariable Calculus

Fundamental Theorem of Conservative Vector Fields || Multivariable Calculus (Assignment 11, pt 1)

turksvids 2023-05-27 | Assignment 11, part 1.

In this video we use the fundamental theorem of conservative vector fields to evaluate line integrals. First we do the line integral the long way (direct substitution), then we use the fundamental theorem.

These are fully worked out problems with commentary.

This is a common topic in Calculus III, Multivariable Calculus

2023 AP Calculus BC FRQ #6

turksvids 2023-05-11 | 2023 AP Calculus BC Exam Free Response Question #6
Taylor Series Problem!

Topics: product rule with function notation; evaluating derivatives; constructing Taylor/Maclaurin polynomial; Lagrange error bound; Taylor polynomial based on previous polynomial

2023 AP Calculus BC FRQ #5

turksvids 2023-05-11 | 2023 AP Calculus BC Exam Free Response Question #5
Miscellaneous Calc BC Topics!

Topics: area; natural logs; improper integral (notation matters!); integration by parts

2023 AP Calculus BC FRQ #2

turksvids 2023-05-11 | 2023 AP Calculus BC Exam Free Response Question #2
Parametric Equations/Vectors

Topics: acceleration vector; speed; solving equation with speed; slope of tangent line; position from velocity (FTC); distance traveled; calculator active

I use the TI-Nspire CXII CAS for all my videos. See here for how to use it on the AP Calculus exam: youtu.be/S0jcV33CLCw

2023 AP Calculus AB FRQ #6

turksvids 2023-05-10 | 2023 AP Calculus AB Exam Free Response Question #6
Implicit Differentiation

Topics: implicit (d/dx); horizontal tangent line; vertical tangent line; related rates (d/dt)

2023 AP Calculus AB FRQ #5

turksvids 2023-05-10 | 2023 AP Calculus AB Exam Free Response Question #5
Miscellaneous Calculus Topics and a Table

Topics: chain rule; product rule; concave up or down; evaluate definite integral; Fundamental Theorem of Calculus (FTC); 2nd Fundamental Theorem of Calculus (2nd FTC); increasing/decreasing/neither at a point

2023 AP Calcululs AB & BC FRQ #4

turksvids 2023-05-10 | 2023 AP Calculus AB & AP Calculus BC Exam Free Response Question #4
Function Analysis (Working with the first derivative)

Topics: max/min/neither; intervals concave down from f’; limit; l’hopital’s rule (l’hospital’s rule); absolute minimum (candidates test)

See more about L’Hospital’s Rule on the AP Exam here: youtu.be/0upI8xpYWLM

2023 AP Calculus AB & BC FRQ #3

turksvids 2023-05-10 | 2023 AP Calculus AB & AP Calculus BC Exam Free Response Question #3
The Milk Problem! (Differential Equations)

Topics: solution curve on slope field; tangent line approximation; second derivative (implicit differentiation); overestimate or underestimate; separation of variables; particular solution

2023 AP Calculus AB FRQ #2

turksvids 2023-05-10 | 2023 AP Calculus AB Exam Free Response Question #2

Particle Motion/velocity & acceleration problem!

Topics: changing direction based on velocity; acceleration; speed increasing/decreasing; distance between position at two times (displacement); total distance from velocity; calculator active

I use the TI-Nspire CXII CAS for all my videos. See here for how to use it on the AP Calculus exam: youtu.be/S0jcV33CLCw

2023 AP Calculus AB & BC FRQ #1

turksvids 2023-05-10 | 2023 AP Calculus AB & AP Calculus BC Exam Free Response Question #1

Table/Working with Rate Hybrid problem!

Topics: Interpret definite integral of rate in context; right Riemann sum; MVT (Rolle’s Theorem); average value; derivative on calculator; interpret derivative in context

For help interpreting derivatives in context see this video: youtu.be/GN-88JqU9Ss
I use the TI-Nspire CXII CAS for all my videos. See here for how to use it on the AP Calculus exam: youtu.be/S0jcV33CLCw

AP Calculus AB/BC Multiple Choice Practice Test (2012 AP CED Problems)

turksvids 2023-04-16 | In this video we do 24 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document (which was called the Curriculum Framework back then). I've always called it "The Acorn Book" but I don't think it's the official name. Not enough people know about these problems! These are from the 2012-2013 version.

I've included complete solutions, discussion, and helpful hints along the way. Using actual CB problems is the best way to practice for the AP Calculus exam's multiple choice section!

Topics: limit definition of derivative; signs of first and second derivative; implicit differentiation; volume of revolution; sign chart/function analysis; chain rule; separable differential equations; average rate of change; speed increasing/decreasing; antiderivatives; limits to infinity; area of regions; second fundamental theorem (2nd FTC); slope fields; radial density function; continuity; interpreting from table; velocity; accumulation functions; average value; local linear approximation; integral of rate for total; fundamental theorem (impossible integral)

#apcalculus #apexams

AP Calculus BC Multiple Choice Practice Test (2016 AP CED Problems)

turksvids 2023-04-12 | In this video we do 8 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document (which was called the Curriculum Framework back then). I've always called it "The Acorn Book" but I don't think it's the official name. Not enough people know about these problems! These are from the 2016-2017 version.

I've included complete solutions, discussion, and helpful hints along the way. Using actual CB problems is the best way to practice for the AP Calculus exam's multiple choice section!

Topics: slope of parametric curve (dy/dx); Euler's Method; improper integrals; integration by parts (IBP); alternating series error; Taylor series coefficients; Taylor's formula; nth term of Taylor series; conditional and absolute convergence; distance traveled for parametric & vector valued functions; integral test & left Riemann sums

#apcalculus #apexams

AP Calculus Multiple Choice Practice Test (2016 AP CED Problems)

turksvids 2023-04-09 | In this video we do 16 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document (which was called the Curriculum Framework back then). I've always called it "The Acorn Book" but I don't think it's the official name. Not enough people know about these problems! These are from the 2016-2017 version.

I've included complete solutions, discussion, and helpful hints along the way. Using actual CB problems is the best way to practice for the AP Calculus exam's multiple choice section!

Links to additional useful videos:
Problem 1 (L'Hospital's): youtu.be/wdmUfyC3XT4
Problem 5 (slope field): youtu.be/hR0JdI9V6wQ
Problem 8: (Limits of Riemann sums): youtu.be/QkzH8NVecgQ
Problem 10 (separable diff eq): youtu.be/C7CWd8boRy0
Problem 13 (interpret derivative): youtu.be/GN-88JqU9Ss
Problem 14 (IVT & MVT): youtu.be/gDn9meEwqCI

Topics: L'Hopital's Rule (L'Hospital's Rule); limit to infinity without L'Hopital's; continuity & differentiability; related rates (volume, surface area); slope field of differential equation; definition of derivative; second fundamental theorem (2nd FTC); limit of Reimann sum for definite integrals; average value; separable differential equations; matching a graph to its derivative; increasing & decreasing; interpreting a derivative; MVT & IVT conditions; integrating a rate to get total (accumulation functions); distance traveled

#apcalculus #apexams

AP Calculus Multiple Choice Practice Test (2020 AP CED Problems)

turksvids 2023-04-07 | In this video we do 22 AP calculus multiple choice problems from the College Board's AP Calculus AB & BC Course and Exam Description document. I've always called it "The Acorn Book" but I don't think it's the official name. Not enough people know about these problems! These are from the 2020 version.

Find the document here:
apcentral.collegeboard.org/courses/ap-calculus-ab

I've included complete solutions, discussion, and helpful hints along the way. Using actual CB problems is the best way to practice for the AP Calculus exam's multiple choice section!

Topics: L'Hopital's Rule (L'Hospital's Rule); Differentiability at a point; product rule; implicit differentiation; related rates; limit of Riemann sum; second (2nd) FTC; u-substitution; slope fields; area (with respect to y); one-sided limits; acceleration from velocity; inferences from tables; points of inflection; integrating rate to get total; integration by parts; logistic differential equation; second derivative of parametric equations; conditional convergence; taylor/maclaurin series; polar area; Lagrange Error Bound

#apcalculus #apexams

Calc AB Review Quiz 7 (2023)

turksvids 2023-03-29 | Link to pdf of all review quizzes: bit.ly/3mUnIlU

In this video we go over AP Calculus Review Quiz #7 for 2023.
Full voice over explanations.

Topics: slope fields; sketching solution curves; concavity of solution curves; relative extrema (2nd derivative test); tangent lines; approximations; finding m and b so y=mx+b is a solution; finding particular solutions; finding values to make something a solution; caring about the range of a solution curve; factoring out a negative leading coefficient

#apcalculus #apexams #calculus

Calc BC Review Quiz 1 (2023)

turksvids 2023-03-26 | Link to pdf of all review quizzes: bit.ly/3mUnIlU

In this video we go over AP Calculus Review Quiz #1 for 2023.
Full voice over explanations.

Topics: parametric/vector functions; speed; acceleration vector; tangent line; polar coordinates; polar area; tangent line to polar curve; describing motion along a polar curve (relative to x and y axis and origin); taylor polynomials; taylor polynomial by composition; integral of taylor polynomial; exact values from taylor polynomials

#apcalculus #apexams #calculus

Song during TI-Nspire parts is Cinematic Africa from
no-copyright-music.com/happy-inspirational
(highly recommend that site!)

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 6)

turksvids 2023-03-22 | Assignment 10, part 6.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 31
3:54 Number 32
7:47 Number 35

This is a common topic in Calculus III, Multivariable Calculus

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 5)

turksvids 2023-03-21 | Assignment 10, part 5.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 27
1:56 Number 28
4:11 Number 29
5:56 Number 30

This is a common topic in Calculus III, Multivariable Calculus

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 4)

turksvids 2023-03-20 | Assignment 10, part 4.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 23
2:09 Number 24
4:49 Number 25
6:14 Number 26

This is a common topic in Calculus III, Multivariable Calculus

AP Calc Problem Set of the Day 133

turksvids 2023-03-17 | Link to problems: drive.google.com/file/d/1r7vCERKksRYs4c0qVM2fgXVKXlAujcuA/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
related rates (the shadow problem); L'Hopital's Rule (L'Hospital's Rule); separable differential equation

#apcalculus
#apcalc

AP Calc Problem Set of the Day 132

turksvids 2023-03-16 | Link to problems: drive.google.com/file/d/1LQ0mFxnWko6RIfTj0o4-F9pHj9BhzfdJ/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
definite integral over jump discontinuity; complete the square to integrate; second FTC

#apcalculus
#apcalc

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 3)

turksvids 2023-03-15 | Assignment 10, part 3.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 19
2:06 Number 20
4:46 Number 21
7:58 Number 22

This is a common topic in Calculus III, Multivariable Calculus

AP Calc Problem Set of the Day 131

turksvids 2023-03-15 | Link to problems: drive.google.com/file/d/1t874myqZS1dwS0x3UQIVkSP-OIWId_ob/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
volume of solid of revolution; properties of definite integrals; u-substitution; solving a differential equation

#apcalculus
#apcalc

AP Calc Problem Set of the Day 130

turksvids 2023-03-14 | Link to problems: drive.google.com/file/d/1mBFjdgtjQHh3EJ0ZTtTXVUr3SF7CFHxt/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
tangent to reciprocal of function; make function continuous; definite integral; limit definition of derivative

#apcalculus
#apcalc

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 2)

turksvids 2023-03-13 | Assignment 10, part 2.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 6
2:57 Number 7
4:50 Number 8
7:16 Number 15
9:20 Number 16
12:20 Number 17
13:46 Number 18

This is a common topic in Calculus III, Multivariable Calculus

AP Calc Problem Set of the Day 129

turksvids 2023-03-13 | Link to problems: drive.google.com/file/d/1F4xj-KTA0LblTZOG8PzZOUKXhRqiJeZK/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
given graph of first derivative; second FTC; value of accumulation function; increasing/decreasing; concavity; quotient rule; tangent line; particular solution to differential equation

#apcalculus
#apcalc

AP Calc Problem Set of the Day 128

turksvids 2023-03-10 | Link to problems: drive.google.com/file/d/12EtpGsb0AlwQr4vRJiEFE4gmVFTvGJdG/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
average value; volume of revolution; finding solution to differential equation of form y=mx+b; second derivative of implicit

#apcalculus
#apcalc

AP Calc Problem Set of the Day 127

turksvids 2023-03-09 | Link to problems: drive.google.com/file/d/1i4k3ycr8yv2x1qOYrVw3A4F2wUUccGde/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
calculator; speed increasing/decreasing; times a particle turns around; position from velocity; total distance traveled; particular solution to separable differential equation

#apcalculus
#apcalc

Tons of Line Integrals || Multivariable Calculus (Assignment 10, pt 1)

turksvids 2023-03-08 | Assignment 10, part 1.

In this video we find a whole lot of line integrals--both scalar and vector fields. Once you get the hang of it, they're not that bad, just lots of substitutions and remembering what to do and when.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 1
4:07 Number 3
7:36 Number 4
9:54 Number 5

This is a common topic in Calculus III, Multivariable Calculus

AP Calc Problem Set of the Day 126

turksvids 2023-03-08 | Link to problems: drive.google.com/file/d/1rw7BHhQPurItL3iMMFFqZAuFrQQPlWxD/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
tangent line; particular solution to separable differential equation

#apcalculus
#apcalc

Particular Solutions to Separable Differential Equations Practice #openstax 4.3 133-142

turksvids 2023-03-07 | In this video we do problems 133 through 142 of Section 4.3 Separable Differential Equations. In all problems I color coded the work so that it's easy to follow. These are initial value problems in which we are finding the particular solution. (That just means solve for C.) A couple of notes:
Problems 136, 138, and 139 are Calc BC only
Problem 137 is just random calculus and NOT Calc AB or BC material.

Separable differential equations are a very common application of integrals (I'm calling them that!) in both Calc 1 and Calc 2 (Calc AB and Calc BC).

Here's a link to the section:
openstax.org/books/calculus-volume-2/pages/4-3-separable-equations
It's an excellent resource and I highly recommend it!

citation:
Access for free at openstax.org/books/calculus-volume-2/pages/1-introduction

#calculus #apcalculus #openstaxcalculus #openstax

AP Calc Problem Set of the Day 125

turksvids 2023-03-07 | Link to problems: drive.google.com/file/d/1luw2x1ksKnBMd_pLRpcc8_7ORm-TmtOp/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
particular solution to separable differential equation; integrating density function; tangent line

#apcalculus
#apcalc

Finding Potential Functions by Inspection || Multivariable Calculus (Assignment 9)

turksvids 2023-03-06 | Assignment 9.

In this video we find potential functions for vector fields (or find that none exists) by inspection (whatever that means). In some we integrate one of the partial derivatives and then take derivatives. In some we integrate each of the partial derivatives. In a couple we show the mixed partials are not equal and so no potential function exists.

These are fully worked out problems with commentary.

Time stamps:
0:00 Number 39
2:03 Number 40
5:10 Number 41
5:48 Number 42
8:04 Number 43
9:40 Number 44
11:49 Number 45

This is a common topic in Calculus III, Multivariable Calculus

AP Calc Problem Set of the Day 124

turksvids 2023-03-06 | Link to problems: drive.google.com/file/d/1SWU7j3rfZ86EwVocxZ02AWcp4tMNxCer/view?usp=sharing
Link to playlist: youtube.com/playlist?list=PL6iwkLfBjZixpMIxRGIO2j3Ku8ZSW5wf9

Topics:
volume of solid with known cross sections (equilateral triangle; semicircle; area of cross given); integral of absolute value; limit of abs(x)/x

#apcalculus
#apcalc

Separable Differential Equations Practice #openstax 4.3 119-132

turksvids 2023-03-05 | In this video we do problems 119 through 132 of Section 4.3 Separable Differential Equations from the OpenStax Calculus Volume 2. In all problems I color coded the work so that it's easy to follow.

Separable differential equations are a very common application of integrals (I'm calling them that!) in both Calc 1 and Calc 2 (Calc AB and Calc BC).

Here's a link to the section:
openstax.org/books/calculus-volume-2/pages/4-3-separable-equations
It's an excellent resource and I highly recommend it!

citation:
Access for free at openstax.org/books/calculus-volume-2/pages/1-introduction

#calculus #apcalculus #openstaxcalculus #openstax

Chain Rule Practice Problems

turksvids 2023-03-04 | In this video we do four really good chain rule problems in preparation for the AP Calculus AB and AP Calculus BC exams. Being comfortable with the different notations is essential if you're going to ace the AP exams!

Differential Equation Solver TI-Nspire CXII CAS

turksvids 2023-03-03 | A short showing how to use the differential equation solver on the TI-Nspire CXII CAS. Great feature. Highly recommended.

#shorts #apcalculus #calculus #tinspire #differentialequation