NapkinCalc

Multivariable Calculus — Vectors & Gradients

Finding a minimum

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: a low point of a landscape is flat in every directionall partial derivatives are zero. The bowl f(x, y) = x² + y² bottoms out at the origin (0, 0), where its height is 0 and nowhere nearby is lower.

✓ pass f2(0,0)==0andf2(0,0)<=f2(0.1,0.1)f2(0, 0) == 0 and f2(0, 0) <= f2(0.1, 0.1) the origin really is the bottom of the bowl

Where next: Proofs & Logic — the rules of reasoning that make every theorem above certain, not just plausible.