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$$ f_{(x,y)} = x^2 - 2y^2 + 3x $$

In what direction from (1,2) should we proceed so that the change so that the change in f in that direction would increase most rapidly?

I'm guessing you would have to maximize the Fx and Fy, other than that I'm pretty much lost.

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up vote 0 down vote accepted

The gradient of a function points in the direction of steepest ascent.

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so I did that and I have: <2x +3 , -4y> for the gradient. – 40Plot Oct 2 '12 at 2:23
That's right. So now you want to evaluate that at the point (1,2). – Zach L. Oct 2 '12 at 2:25
right, so it's <5,-8>. and so that's the direction vector of f? – 40Plot Oct 2 '12 at 2:28

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