Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 5 x ; a = 1

h=1 df/dx=-15

h=0.1 df/dx=-10.5

h=0.01 df/dx=-10.05

h=0.001 df/dx=-10.005

h=0.0001 df/dx=-10.0005

Step-by-step explanation:

The function should be 5x^2.

If the function is linear, the answer is very simple: it is 5 for every value of h.

The rate of change can be defined as:

For this function f=5x we have:

Then, we have:

The value for a is a=1

For h=1

For h=0.1

For h=0.01

For h=0.001

For h=0.0001