Homework Statement
Give an example of a continuous function f:R^2→R having partial derivatives at (0,0) with
f_1 (0,0)≠0,f_2 (0,0)≠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.
(If this is too difficult...