I tutor people in a variety of math subjects, but had a Calc III question come up that I could not remember quite how to do, nor could I find a reference to check.
Suppose you are standing on a hill given by $h(x,y)=-x^2-y^2-10$, at the point $(1,1,8)$. If you take a step in the direction of steepest descent, where do you end up, as a point $(x,y,h)$
I know the direction of steepest descent is the negative of the gradient, I know that "a step" is taken to mean a differential step, but just the last bit, to find how far you actually move down the hill when you move a differential step in that direction, has got me.