Question

MAC2313 Assigment 3 (Sping 2013 NAME Ony ana pebat vill be fuly graded so rake sare to do all of them 2. Masimue he funcion TCH w)-3u-2+won the sphere u2 + 14 wh the mehod of Lagrange Ths b easest done MAC2313 Assignment 3 /Spring 2019 (5 points) NAME Instructions: Please provide the solution of each of the following problems cleary and identifiying each by its number Only one problem wil be fully graded so make sure to do all of them 1. (a) On the lines below, precisely state the Extreme Value Theorem: (b) Find the extreme values of the function fxy)x2y-2x-2y+4 on the closed disk D- f(x,y)lx2 +y' s 9). Hint: a better way of handing the boundary is to parametrize the circle wih- 3 cos t, y- 3 cos t. Then the function f becomes a function af t on the boundary and you can use the calculus of a single variable to find its extreme values 2 Maximize the function T(u,,w) 3u-2v+ w on the sphere u2+ with the method of Lagrange + w 14. This is easiest done

Answer 1

1. a) If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the extremum occurs at a critical point.

b)

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95 C-642 J2. 3-62 32P 2 2. 11 =