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For each of the following functions, find the maximum and minimum values of the function on the rectangular region: . Do this by looking at level curves and gradiants. f(x,y) =x+y+3: f(x,y) = 3x2 + 4y2: =f(x,y)=(4)2x2-(3)2y2:

Solution

A)

maximum value = 3+4+3 = 10

minimum value = -3-4+3 = -4

B)

maximum value = 3*3^2+4*4^2 = 27 + 64 = 91

minimum value = 3*0^2+4*0^2 = 0+0 = 0

C)

maximum value = 4^2*3^2-3^2*0^2 = 16*9 - 0 = 144

minimum value = 4^2*0^2-3^2*4^2 = 0-144 = -144