Subjects / Calculus III
Calculus III: Multivariable Differentiation
Without this course you would maximize a function on a constraint the hard way: walk along g(x,y)=c, plug each pair into f(x,y), and hope you hit the peak. The intro puzzle makes that pain visceral — then shows the contour-tangency “cheat code” and lifts it into 3D so you know what you are aiming at.
Stage 1
Blind probe along the constraint — feel why brute force fails.
Stage 2
Grow level sets until they kiss the curve — ∇f = λ ∇g.
Stage 3
Unveil 3D: the tangent point is the ridge peak on z = f(x,y).