Question

Given the function f(x) = 4x - 2, explain and show how to find the average rate of change between x = 2 and x = 4.

Answer 1

Answer:

The average rate of change between x = 2 and x = 4 is of 4.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function f(x) in an interval [a,b] is given by:

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

In this question:

$f(x) = 4x - 2, b = 4, a = 2$

Thus:

$f(b) = f(4) = 4(4) - 2 = 16 - 2 = 14$

$f(a) = f(2) = 4(2) - 2 = 8 - 2 = 6$

Average rate of change:

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

$A = \frac{14-6}{4-2}$

$A = \frac{8}{2}$

$A = 4$

The average rate of change between x = 2 and x = 4 is of 4.