Question

What is the average rate of change for the function f(x) over the interval [0, 3]

Answer 1

Answer:

The average rate of change is 22

Step-by-step explanation:

Given

$f(x) = x^4 - 5x$

Required

Average rate of change over [0,3]

This is calculated as:

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

So, we have:

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

Calculate f(3) and f(0)

$f(x) = x^4 - 5x$

$f(3) = 3^4 - 5 * 3 =66$

$f(0) = 0^4 - 5 * 0 = 0$

So, we have:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{66-0}{3}$

$Rate = \frac{66}{3}$

$Rate = 22$