Question

8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)

Answer 1

i f(1, 1) = a) (contour of Z=- is passing through (-1,1)) i) H3,123 See contour 2=3 & then wh check a coosdinate when it basses through y=1 (x22 ili) f(0,4)=-2 see contour 22-2 & then check y coordinate when it passes through azo ly=1 local maximum at (0,0) because contour values are increasing towards (0,0) increasing towards (90)

The value goes from 1, 2, 3, 4 fx (1,0) Check the values of contours tusht looking at (10)$(20), 622016 The value goes from 1, 2, 3, 4 +(1,0)) 42,0) = 4 Thus fxso fy(0,1) check the values of contours looking at pt (0,1) † (0,1.2), 10, 1-4) at since z decreases. Hence If y(0,1) <0