The figure below shows contours of Find the values of ff on

The figure below shows contours of

Find the values of ff on the contours. They are equally spaced multiples of 10.

Solution

c = f(x,y) = 140e^x-120y²

f(0,0) = 140 = c(0,0) so the contour passing through the origin has f=140.

f(x,y) is continuous so the contours near f=140 are f=150 and 120

f=150 passes through (ln 15/14,0) to the right of f=140.

Thus 120 is the other contour passing through (0,+-sqrt(1/13)) and (-ln 14/12,0), to the left of f=140