Unit vector in direction of max increase of f(x,y,z)

[musicmar]

Homework Statement

Find the unit vector e at P=(0,0,1) pointing in the direction along which f(x,y,z)=xz+e^-x2+y increases most rapidly.

The Attempt at a Solution

In order to find the direction where f increases most rapidly, I found the second derivative of f.
I don't know how to put the curly d's in here, but

<(d²f/dx²,d²f/dy²,d²f/dz²>=<4e^-x2+y,e^-x2+y,0>

The second derivative should be zero where f increases the most rapidly, but I'm not sure what do do with the point or how to set the second derivative equal to zero from this point.

 

[Kevin_Axion]

Here just click on this and copy this code:

$$\frac{\partial^2f}{\partial x^2},\frac{\partial^2f}{\partial y^2},\frac{\partial^2f}{\partial z^2}=4e^{-x^2+y},e^{-x^2+y},0$$ or you can just write $$\nabla^2 f$$

 

[musicmar]

But that doesn't help me answer the question.

 

[Kevin_Axion]

I know I'm only in the 11^th grade and I know very little multi-variable calculus. I was just making the question more presentable so people who have taken this course will have a better reception and hence will answer your question.

 

[musicmar]

Well, thanks for showing me how to enter partial derivatives, anyway.