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
f(x, y) = 3y cos x, 0 ¡Ü x ¡Ü 2¦Ð
what is the saddle point for this?
1 answer