estimate partial derivative of f with respect to x and with

estimate partial derivative of f with respect to x and with respect to y at point A

Consider the contour plot of f(x,y) as shown below.

Solution

as we have to find fx(1,-1)

We can estimate fx by observing that as x goes from 0.5 to 1.5,with y = -1 fixed,

f seems to go from about 0.5 to 0.4

Therefore fx(1, -1) is approximately -0.1