# Thread: Derivative / slope related question

1. ## Derivative / slope related question

Hi,

I have a problem stated as such:

"The elevation of a mountain above sea level at (x,y) is given as 3000e^(-(x^2 + 2y^2)/100) meters. Sea level is represented by the xy-plane and the positive x-axis points east, the positive y-axis points north. The climber is directly above (10,10). If they move northwest, will they ascend or descend and at what slope?"

So, I've figured out that the climber will descend. And I'm sure that to find the slope I need to take some form of derivative. I'm just not sure what to derive with respect to. I'm thinking I should take the partial of X plus the partial of Y, but I'm not sure.

Is that the best approach?

2. Originally Posted by Katzenjammer
Hi,

I have a problem stated as such:

"The elevation of a mountain above sea level at (x,y) is given as 3000e^(-(x^2 + 2y^2)/100) meters. Sea level is represented by the xy-plane and the positive x-axis points east, the positive y-axis points north. The climber is directly above (10,10). If they move northwest, will they ascend or descend and at what slope?"

So, I've figured out that the climber will descend. And I'm sure that to find the slope I need to take some form of derivative. I'm just not sure what to derive with respect to. I'm thinking I should take the partial of X plus the partial of Y, but I'm not sure.

Is that the best approach?
NW is in the direction of the unit vector: $\bold{u}=(-\sqrt{2},\sqrt{2})$

The required slope is:

$
s=\left. \nabla f(x,y) . \bold{u} \right|_{x=10,y=10}
$

where $f(x,y)$ is the function specifying the shape of the mountain.

CB