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?
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