Question

Find the average rate of change of f(x)=9x^2−8 on the interval [1,b] . Your answer will be an expression involving b

Answer 1

Given:

Function is

$f(x)=9x^2-8$

On interval [1, b]

Required:

Find the average rate of change?

Explanation:

The average rate change of f(x) on the interval. [a, b] is

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

We have that a = 1, b = b,

$f(x)=9x^2-8$

Thus

$\begin{gathered} \frac{f(b)-f(a)}{b-a}=\frac{-8+9b^2-(-8+91^2)}{b-(-1)} \\ =\frac{9b^2-9}{b-1} \\ =9b+9 \end{gathered}$

Answer:

Hence, this is the answer.