Question

A geologist in Tibet discovers a new mountain in the area of Gyangtse. The equation of the mountain is given by f(x,y) = -x^4 - y^4 +2xy where x and
y is measured in mile. What is the
relative maximum height of the mountain in meters?

Answer 1

you need
Fx = 0 and Fy=0 for a max, so
-4x^3 + 2y = 0
-4y^3 + 2x = 0

max f=1/2 at x = y = ±1/√2

Answer 2

(1137.967, 1137.967) meters