1. ## Tangent planes

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!

2. Originally Posted by HFLER
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!
If the tangent plane is horizontal to the surface then the normal to the plane will be $\vec{n} = \pm k$.

3. All the directional derivatives must be zero.
Hence all partial derivatives must be zero.

BUT $f_x=e^x\ln y$ and $f_y={e^x\over y}$ are never zero.

We can let y=1, but $f_y={e^x\over y}$ is never zero, I should say.