Partial 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.

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.