MATH 126- Final Exam Guide - Comprehensive Notes for the exam ( 81 pages long!)
Document Summary
An absolute/global maximum over r is the largest z-value over r. An absolute/global minimum over r is the smallest z- value over r: key fact (extreme value theorem): The absolute max/min must occur at either: a critical point, or, a boundary point, example: let r be the triangular region in the xy-plane with corners at (0, -1), (0, 1), and (2, -1) Find the absolute max and min over this region r for the surface: f(x, y) = 1/4x2 + 1/2y2 xy + 1. 2: solving these types of problems, step 1: find critical points inside region, step 2: boundaries (the triangle from the previous problem has. I) give equation in terms of x and y. Objective: minimize distance from (x, y, z) on the cone to the point (4, 2, 0) give that z2=x2+y2: dist = f(x, y, dist = sqrt((x-4)2+(y-2)2+z2, f(x, y) = sqrt((x-4)2+(y-2)2+x2+y2)
