allsmiles
Give the unit vector that has the direction of maximum increase of the function .
f(x, y) at the location (−2, 1). For f(x,y)=x^2+2y^2y



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surdawi
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plug in x and y

surdawi
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f(2,1)=(2)^2+2*1^21

TuringTest
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you will need the gradient first I think

allsmiles
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Yeah is the answer not the gradient divided by the mag?

allsmiles
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to get the unit vector? Since the max increase is in the same direction as the gradient?

TuringTest
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yes, it should be gradient divided by magnitude

TuringTest
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well, the gradient is the maximum direction of change; could be increase or decrease

allsmiles
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so how do you know if it's increase or decrease?

TuringTest
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I'm actually not too sure in this case. You could do it with multivariable max/min techniques if you know them.

allsmiles
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alright man thanks for your help much appreciated

TuringTest
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welcome