Question

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.) (Round your answers to five decimal places.)

Answer 1

The average rates of change of the function are listed below:

1. r = -0.19047
2. r = - 0.21850
3. r = - 0.22185
4. r = - 0.22219
5. r = - 0.22222

How to calculate the average rate of change of a function over an interval?

Herein we must determine the average rate of change of a function over a given x-value, which can be found by using the secant line formula:

r = [f(a + h) - f(a)] / h

Where:

• a - x-value associated to the function.
• h - Change in x-value.

If we know that f(x) = 8 / x and a = 6, then the average rate of change of the given function for different values of h:

f(6) = 8 / 6

f(6) = 1.33333

h = 1

f(7) = 8 / 7

f(7) = 1.14286

r = (1.14286 - 1.33333) / 1

r = -0.19047

h = 0.1

f(6.1) = 8 / 6.1

f(6.1) = 1.31148

r = (1.31148 - 1.33333) / 0.1

r = - 0.21850

h = 0.01

f(6.01) = 8 / 6.01

f(6.01) = 1.33111

r = (1.33111 - 1.33333) / 0.01

r = - 0.22185

h = 0.001

f(6.001) = 8 / 6.001

f(6.001) = 1.33311

r = (1.33311 - 1.33333) / 0.001

r = - 0.22219

h = 0.0001

f(6.0001) = 8 / 6.0001

f(6.0001) = 1.33331

r = (1.33331 - 1.33333) / 0.0001

r = - 0.22222

To learn more on average rates of change: https://brainly.com/question/23715190

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