f(x,y) as a surface:
as seen f(x,y)=0 can be considered as extreme value.
Local extremes perhaps can have meaning for x=constant:
I am having trouble finding the local extremes for a particular function.
f(xy)=e^(2x)cosy
I have so far:
f'(x)= 2e^(2x)cosy
f'(y)=-e^(2x)cosy
f''(x)=4e^(2x)cosy
f''(y)=-e^(2x)cosy
f''(xy)=-2e^(2x)siny
Now I'm setting both f'(x) and f'(y) = 0, but this is where I'm having trouble. Does that mean that 2e^(2x)=0, cosy=0, -e^(2X)=0, and siny=0?
Thanks for any help that can be provided.