I am asked to locate all relative maxima and minima and saddle points of the following function:

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

I found the first partials:
fx=(e^x)siny

fy=(e^x)cosy

If:

(e^x)siny=0 and (e^x)cosy=0

Why does my book say there are no critical points?

Question

I am asked to locate all relative maxima and minima and saddle points of the following function:

f(x,y)=(e^x)sin(y) 

I found the first partials:
fx=(e^x)siny 

fy=(e^x)cosy 

If: 

(e^x)siny=0 and (e^x)cosy=0 

Why does my book say there are no critical points?

babyslapmafro · Answer

Is it because given any value for (y), both sin(y) and cos(y) cannot equal 0 simultaneously?