f(x, y) = 3y cos x, 0 ¡Ü x ¡Ü 2¦Ð

what is the saddle point for this?

1 answer

For F(x,y) = 3y cosx, we have

Fx = -3y sinx
Fy = 3 cosx

Fxx = -3y cosx
Fyy = 0

Fxy = -3 sinx

So, for a saddle point, we need

Fx = 0 true for x=0,pi or y=0
Fy = 0 true for x=pi/2, 3pi/2 and all y

Fxx * Fyy - (Fxy)^2 < 0

-3y cosx * 0 - (-3 sinx)^2 < 0
true for all x.

The graph is at

http://www.wolframalpha.com/input/?i=3y*cosx