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Math Help - Partial Derivatives

  1. #1
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    Partial Derivatives

    Give an example of a continuous function from R^2 having partial derivatives at (0,0) with f_1 (0,0) \neq 0 and f_2 (0,0) \neq 0 but the vector (f_1 (0,0) , f_2 (0,0))does not point in the direction of maximal change, even though there is such a direction.
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  2. #2
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    Re: Partial Derivatives

    I take it that you are to do this, not me! Certainly, such a function will have to have discontinuous first derivatives so you might want to think in terms of continuous functions for which the derivative goes to infinity. Something like x^{1/2} comes to mind.
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