Directional Derivatives Question

Question

A bushwalker is climbing a mountain, of which the equation is $f(x,y)=400-\frac{x^2+4y^2}{10000}$. The buswalker is at a point P=(-1600,-400). What is the slope of the mountain at P in the direction of the peak?

I'm having trouble computing the vector for the peak. The rest should be straight forward.

Answer 1

HINT

• find the coordinates of the peak $Q(a,b)$, that is the point of maximum for $f$ (we don't need derivatives to guess it)
• determine the gradient vector $\nabla f(P)$ at $P(-1600,-400)$ and recall that for a given direction expressed by the normal vector $\vec v$ the slope is given by $\nabla f(P)\cdot \vec v$