MATH U101 · Narrated walkthrough · Module 5 §14.5
Tutorial 6 Q11–Q12, from zero
A slow, narrated lesson on the two hardest questions of Sheet 6: recovering the gradient from two measured rates (Q11), and why ∇f · u gives the wrong answer at a piecewise point (Q12). Every substitution is said out loud. Press play, keep the sound on, and answer the four questions it stops to ask you.
About eleven minutes, watch once (use ⏮ ⏭ to replay a scene). The narration stops four times to ask what the next move is. Commit to an answer before it continues: those pauses are the point, because they practise starting a question, not following one. Captions are on by default; the full transcript is below the player.
The same two questions in writing, with figures and a turn-the-direction widget: Tutorial 6 Q11–Q12, from zero. Short solutions: tutorial companion. Q8–Q10 are in the gradient walkthrough (W4). Then redo Q11 and Q12 on paper without looking.