# Partial Derivatives

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• May 7th 2012, 11:29 AM
monomoco
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.
• May 8th 2012, 11:20 AM
HallsofIvy
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.