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

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 $\displaystyle x^{1/2}$ comes to mind.