Find the rate of change

Question

A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - x^2), Where x and f(x) are measured in miles. Find the rate of change of elevation at x = 2.

Answer 1

For figure 3:

Step 1:

The function is

Rate of change of a function is the first derivative of the function .

Differentiating on each side with respect to .

Power rule of derivatives :

Step 2:

Rate of change of elevation at is .

.

Solution:

Rate of change of elevation at is 0.16.

Answer 2

For figure 4:

Step 1:

The function is

Rate of change of a function is the first derivative of the function  .

Differentiating on each side with respect to .

Power rule of derivatives:  

Step 2:

Rate of change of elevation at is .

.

Solution:

Rate of change of elevation at is 0.08 .