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.
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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Posted - 10/08/2007 : 20:26:53
in which the directional derivative of the function f(x,y)=xy + y^2 at point (1,1) is maximum?
mag.u cos 
10 and for <cos 
