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...
Math 210 Lecture 9: Optimization and
Lagrange multipliers
Daniel Ingebretson
University of Illinois at Chicago
July 1, 2024
,Unbounded domains
What’s the absolute maximum of f (x) = 1 − x 2 on
−∞ < x < ∞?
, Example: optimization on an unbounded domain
Find the point on the plane x + 2y + z = 2 closest to the
point (2, 0, 4).
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