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Date Posted: 7/23/2008 3:19:56 PM  Status: Closed
directional derivative
Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:

Consider the function f(x,y) = x^2 +2xy^2


What is the angle θ for which f increases the fastest?

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Date Posted: 8/13/2008 5:00:29 AM  Status: Live
Asker's Rating: Helpful   
Response:
A sketch:
Taking the two dimensional gradient: (2x+2y2,4xy), shows the curve x=y2 is maximum direction for the curve, that is x positive and taking into account that f(x,y) is quadratic only in y. f(y2,y)=3y4.



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