Wrath of Math | Rolle's Theorem Explained (with proof) | Calculus 1 @WrathofMath | Uploaded 1 month ago | Updated 1 hour ago
We introduce Rolle's theorem which we will later use in a proof of the Mean Value theorem. Rolle's theorem states that if a function is continuous on [a,b] and differentiable on (a,b), and f(a)=f(b), then there exists a point c in (a,b) so that f'(c)=0, that is - a place where the derivative is 0. We'll prove Rolle's theorem and go through two examples of using Rolle's theorem. In the first example we will find two x-intercepts of our function then use Rolle's theorem, and in the other example we will use Rolle's theorem to prove a cubic has only one root. #calculus1 #apcalculus
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0:00 Intro
0:15 Rolle's Theorem
1:00 Rolle's Theorem Visualized
2:27 Proof of Rolle's Theorem
5:33 Example 1 of using Rolle's Theorem
7:30 Example 2 of using Rolle's Theorem
10:25 Conclusion
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Outro music by Ben Watts and is available for channel members.
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We introduce Rolle's theorem which we will later use in a proof of the Mean Value theorem. Rolle's theorem states that if a function is continuous on [a,b] and differentiable on (a,b), and f(a)=f(b), then there exists a point c in (a,b) so that f'(c)=0, that is - a place where the derivative is 0. We'll prove Rolle's theorem and go through two examples of using Rolle's theorem. In the first example we will find two x-intercepts of our function then use Rolle's theorem, and in the other example we will use Rolle's theorem to prove a cubic has only one root. #calculus1 #apcalculus
Join Wrath of Math to get exclusive videos, lecture notes, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
Calculus 1 Exercises playlist: youtube.com/playlist?list=PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx
Calculus 1 playlist: youtube.com/playlist?list=PLztBpqftvzxWVDpl8oaz_Co6CW50KtGJy
Get the textbook for this course! amzn.to/3PieD1M
0:00 Intro
0:15 Rolle's Theorem
1:00 Rolle's Theorem Visualized
2:27 Proof of Rolle's Theorem
5:33 Example 1 of using Rolle's Theorem
7:30 Example 2 of using Rolle's Theorem
10:25 Conclusion
★DONATE★
◆ Support Wrath of Math on Patreon: patreon.com/join/wrathofmathlessons
◆ Donate on PayPal: paypal.me/wrathofmath
Outro music by Ben Watts and is available for channel members.
Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● TikTok: tiktok.com/@wrathofmathedu
● X: https://x.com/wrathofmathedu
● Facebook: facebook.com/WrathofMath
