Question

Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x3 + 4. Include the average rate of change in your answer.

Answer 1

In this question, we want to find the average rate of change of a function over an interval, it represents by how much f(x) changes when x changes by 1.

Average rate of change:

The average rate of change of a function over an interval [a,b] is given by:

$A = \frac{f(b) - f(a)}{b - a}$

In this question:

$f(x) = 2x^3 + 4$

Between x = 4 and x = 6, so $a = 4, b = 6$. Then

$f(a) = f(4) = 2*4^3 + 4 = 132$

$f(b) = f(6) = 2*6^3 + 4 = 436$

Then

$A = \frac{436 - 132}{6 - 4} = 152$

Thus, the average rate of change of the function is of 152, that is, when x changes by 1, y changes by 152.

For another problem involving an average rate of change, you can check https://brainly.com/question/14481908