Uploaded August 2025 | Updated September 2026, 2 weeks ago
See how to use Cauchy-Schwarz Ineq for this question (w/ written solution if you prefer reading it) here: patreon.com/posts/135937876
Here's a method for finding the minimum and maximum values of a rational function that high school students in Taiwan need to know. We will see how to find the extrema of the function f(x)=(1+2sin(2x))/(4-cos(2x)). Here's how I would solve this extrema question without calculus! Featuring the Weierstrass Substitution & the discriminant of a quadratic equation. This question is from Dcard: https://www.dcard.tw/f/math/p/259454265?cid=43b70891-4e7a-4920-a60d-6b3aa20cf791
Support this channel and get more content ๐ patreon.com/blackpenredpen
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet ร An R Camila L Luupo Farrah Batman 1127 Mathguru ะะผะธััะธะน ะ. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. Zero Jeffrey C J D Chaz W. Ryan Turbo S Arcana Rehan M Lukasz M NaiKang W Kevin Y Gamesh K kelvin P ํ์ฐ ๋ฐ Minda W Erik P Sebastian C Ryan M Billy J Kian S Stormm HOm3l3ss b Nathan Y Aidyn R
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๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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#blackpenredpen #math #calculus #mathtutorials
See how to use Cauchy-Schwarz Ineq for this question (w/ written solution if you prefer reading it) here: patreon.com/posts/135937876
Here's a method for finding the minimum and maximum values of a rational function that high school students in Taiwan need to know. We will see how to find the extrema of the function f(x)=(1+2sin(2x))/(4-cos(2x)). Here's how I would solve this extrema question without calculus! Featuring the Weierstrass Substitution & the discriminant of a quadratic equation. This question is from Dcard: https://www.dcard.tw/f/math/p/259454265?cid=43b70891-4e7a-4920-a60d-6b3aa20cf791
Support this channel and get more content ๐ patreon.com/blackpenredpen
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet ร An R Camila L Luupo Farrah Batman 1127 Mathguru ะะผะธััะธะน ะ. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. Zero Jeffrey C J D Chaz W. Ryan Turbo S Arcana Rehan M Lukasz M NaiKang W Kevin Y Gamesh K kelvin P ํ์ฐ ๋ฐ Minda W Erik P Sebastian C Ryan M Billy J Kian S Stormm HOm3l3ss b Nathan Y Aidyn R
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๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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#blackpenredpen #math #calculus #mathtutorials
