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

by musicmar
Tags: direction, increase, unit, vector
 P: 100 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 <(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.
 P: 920 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 $$\nabla^2 f$$
 P: 100 But that doesn't help me answer the question.
P: 920

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

I know I'm only in the 11th 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.
 P: 100 Well, thanks for showing me how to enter partial derivatives, anyway.

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