Question

Suppose you are climbing a hill whose shape is given by the equation z = 1300 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (100, 120, 1106). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend

Answer 1

Answer:

a) "ascend"

Step-by-step explanation:

a)

The equation is  $z = 1300-0.005x^2-0.01y^2$

This question is asking for the value of the directional derivative in the direction of -j [since south that's y negative]

So, this is the negative of partial derivative of y. Thus we have:

$z = 1300-0.005x^2-0.01y^2\\z_y=-0.02y$

Now we are at (100,120,1106), we take y value of 120 and put it in the partial:

$z_y=-0.02y\\z_y=-0.02(120)\\z_y=-2.4$

We take the negative, that is -(-2.4) = 2.4

Since this is positive, we can say the hill is sloping upward at this point, so you will start to ascend.