This document is a collection of detailed lecture notes from a university-level course on Multivariable Calculus and Physics. It covers essential topics including lines, planes, and surfaces, projectile motion, limits, partial derivatives, optimization, and integration techniques in various coordin...
,Local extrema of y = f (x)
Let f (x) = x 4 − 2x 3 . Find the critical points and determine
whether each is a local max, local min, or neither.
,Local extrema of z = f (x, y)
, Local extrema of z = f (x, y)
(a, b) in the domain of f is a critical
point if
fx (a, b) = fy (a, b) = 0, or
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