I'm studying for a final exam and reviewing some past exams and just have a small question about this problem.
Part 1 : You are standing at the point $(1,1)$ on a hill whose surface is given by the question $$ z = 5y - x^2 - 2y^2 $$ If you climb in the direction of the steepest ascent what is your rate of ascent with respect to the horizontal distance as you start?
I understood this. You find the gradient vector and then the magnitude of the gradient vector and get the answer
$$\sqrt{5}$$
Part 2: If you decide to go southeast from the point $(1,1)$ on the hill, would you be ascending or descending? At what rate?
You would be descending because your going in a direction away from the gradient vector which points in the direction of the greatest rate of change.
For the rate you would you take the magnitude of $$ 1i -1j $$
$$\sqrt{2}$$
I'm not sure if those was incorrectly marked wrong on my old exam?