MATH U101 · Narrated walkthrough · Module 4 §14.4 Tutorial 6 Q7
Hottest and coldest points on an ellipse, from zero
Tutorial 6, Q7, taught slowly with every step said out loud: where the rate 4 cos 2t comes from, why there are four values of t, how the second derivative says maximum or minimum, and how each t becomes a point. Press play, keep the sound on, and answer the four questions it stops to ask you.
About nine minutes, watch once. This is the slow version of the Q7 part of the rates-along-a-curve walkthrough. The narration stops four times to ask what the next move is. Commit to an answer before it continues: those pauses are the point. Captions are on by default; the full transcript is below the player.
Redo Q7 on paper with the video closed. The written solution, with every step, is in the tutorial companion. The chain-rule tree is in Module 4 notes §5; the same routine on other curves is card 4 of same skeleton, different skin.