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space-wacko
New Member

USA
2 Posts

Posted - 10/08/2007 :  20:26:53  Show Profile
Find direction in which the directional derivative of the function f(x,y)=xy + y^2 at point (1,1) is maximum?

I'm trying to use:gradient vector dot vector u=mag. of gradient mag.u cos .

I found the partials of x and y based on that I pluged in my point to get the gradient vector <1,3>. For my u vector I used <cos ,sin>.For the magnititude I got <1,3>= 10 and for <cos ,sin>=1.

Edited by - space-wacko on 10/08/2007 20:45:58
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pka
Advanced Member

USA
2731 Posts

Posted - 10/09/2007 :  07:46:42  Show Profile
You know that the gradient points in the direction of maximum increase.
Therefore, you want the angle of that vector.
The vector <1,3> has the angle arctan(3) with positive x-axis.

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