Question

What is the average rate of change of the function
f(x) = 2x + 8
over the interval [2, 6)?

Answer 1

The average rate of change of the function f(x) over the interval $[2, 6]$ is 2.

Important information:

• The function is $f(x)=2x+8$.
• The given interval is [2,6].

Average rate of change:

The average rate of change of the function f(x) over the given interval $[a,b]$ is:

$m=\dfrac{f(b)-f(a)}{b-a}$

Using the above formula, we get

$m=\dfrac{f(6)-f(2)}{6-2}$

$m=\dfrac{(2(6)+8)-(2(2)+8)}{4}$

$m=\dfrac{12+8-4-8}{4}$

$m=\dfrac{8}{4}$

$m=2$

Thus, the average rate of change of the function f(x) over the interval $[2, 6]$ is 2.

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