The maximum rate of change is in the direction of the gradient and the max rate of decrease is opposite to the gradient
|fu|= |gradf||u|cos(theta) is a max when theta = 0 recall |u| = 1
Let f be a differentiable function of two variables, and supposed that del f(p) is not the zero vector. For what directions is the directional derivative of f a maximum, a minimum, zero, and half of its maximum value?
I'm not entirely sure how solve this problem.
I know that del f cos theta has a maximum at 1 and a minimum at pi. Is this what the problem is asking?