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Unit vector in direction of max increase of f(x,y,z) 
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#1
Oct1110, 09:18 PM

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 <(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. 


#2
Oct1110, 09:25 PM

P: 921

Here just click on this and copy this code:
[tex]\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[/tex] or you can just write [tex]\nabla^2 f[/tex] 


#3
Oct1110, 09:33 PM

P: 100

But that doesn't help me answer the question.



#4
Oct1110, 09:36 PM

P: 921

Unit vector in direction of max increase of f(x,y,z)
I know I'm only in the 11^{th} grade and I know very little multivariable 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.



#5
Oct1110, 09:41 PM

P: 100

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



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