Find the critical point of the function f(x,y)=2e^x−4xe^y.

Answer 1

critical points are where both partial derivatives are zero. So, you need
Fx = 2e^x - 4e^y = 0
Fy = -4xe^y = 0
so, clearly, x=0, so
e^y = 1/2 ... y = -ln2

the critical point is (0,-ln2)