Find the absolute maximum and minimum of the function f(x,y)=ysqrt(x)−y^2−x+3y on the domain 0≤x≤9, 0≤y≤6.

Answer 1

Fx = y/(2√x) - 1
Fy = √x - 2y+3
Fx = Fy = 0 at (1,2)
But this is a maximum.
So, to find the minimum, check f(x,y) at the four corners of the domain.
f(0,6) = -18