(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

3. 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

<(d^{2}f/dx^{2},d^{2}f/dy^{2},d^{2}f/dz^{2}>=<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.

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

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