Hi guys,
I have a problem: for the equation f(x,y)=e^xln(y), how do I determine if the surface z=f(x,y) has any horizontal tangent planes?
The thing that's tripping me up is the "horizontal" part.
Any help would be most appreciated. Thanks!
Hi guys,
I have a problem: for the equation f(x,y)=e^xln(y), how do I determine if the surface z=f(x,y) has any horizontal tangent planes?
The thing that's tripping me up is the "horizontal" part.
Any help would be most appreciated. Thanks!
All the directional derivatives must be zero.
Hence all partial derivatives must be zero.
BUT $\displaystyle f_x=e^x\ln y$ and $\displaystyle f_y={e^x\over y}$ are never zero.
We can let y=1, but $\displaystyle f_y={e^x\over y}$ is never zero, I should say.