Local min/max/saddle points of 3d graphs

[karadda]

Hello, just got done taking a test and one problem kinda confused me.

Homework Statement

f(x,y) = e^x cos y

find local min/max and saddle points

Homework Equations

fx = e^x cos y
fy = -e^x sin y

The Attempt at a Solution

I answered that there were no critical points for this function and therefore no extrema. I looked at a graph of this here. To me, those sharp crevices indicate the function is not differentiable at those points. Is this correct?

 

[HallsofIvy]

No. $e^x cos(x)$ and $e^x sin(x)$ (and, in fact, are infinitely differentiable) for all x and y. Those peaks look like "sharp crevices" only because your scale is too large.