# Homework Help: Directional derivatives

1. Apr 15, 2012

### NewtonianAlch

1. The problem statement, all variables and given/known data
A bush-walker is climbing a mountain, of which the equation is $h \left( x,y \right) =400-{\frac {1}{10000}}\,{x}^{2}-{\frac {1}{2500} }\,{y}^{2}$

The x-axis points East, and the y-axis points North. The bush-walker is at a point P, 1600 metres West, and 400 metres South of the peak.

What is the slope of the mountain at P in the direction of the peak?

3. The attempt at a solution

I'm fairly sure on how to solve this, except I need a few different elements. Since we have the starting point, I can calculate the gradient at that point. I need to find a directional vector (to the peak) from that point, and that's what I'm not sure to find.

Looking at the equation for the mountain, I'm guessing its peak is when (x,y) = (0,0)

I first tried for v = +1600i + 400j, but that was not correct.