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(See Solution) Suppose you are climbing on a surface whose height is given by the function f(x, y)=x y-3 x^2. You are at the point where x=1, y=5. In what

Question: Suppose you are climbing on a surface whose height is given by the function $f(x, y)=x y-3 x^{2}$. You are at the point where $x=1, y=5$.

In what direction would you proceed to have the maximum rate of increase in your height? At what angle with respect to the horizontal would you initially be ascending if you went in that direction?
In what direction(s) could you proceed so that initially you are not ascending or descending?

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(See Solution) Suppose you are climbing on a surface whose height is given by the function f(x, y)=x y-3 x^2. You are at the point where x=1, y=5. In what

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