Give an example of a continuous function from having partial derivatives at (0,0) with and but the vector does not point in the direction of maximal change, even though there is such a direction.

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- May 7th 2012, 11:29 AMmonomocoPartial Derivatives
Give an example of a continuous function from having partial derivatives at (0,0) with and but the vector does not point in the direction of maximal change, even though there is such a direction.

- May 8th 2012, 11:20 AMHallsofIvyRe: 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 comes to mind.