- #1

musicmar

- 100

- 0

## 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

<(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.