Question

The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x² - 0.004y². A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rate?

Answer 1

i-2.4j

Explanation:

Given that,

The surface of a mountain is modeled by the equation as follows :

`h(x,y)=5000 -0.001x^2-0.004y^2`

A mountain climber is at the point (500, 300, 4390).

We need to find the direction in which he should move in order to ascend at the greatest rate.

To find direction, first finding the gradient of h as follows :

`\\abla h(x,y)=-0.002xi-0.008yj`

Now put x = 500 and y = 300

So,

`\\abla h(x,y)=-0.002(500)i-0.008(300)j\\\\\\abla h(x,y)=i-2.4j`

The direction of the climber is i-2.4j