Question

given the function f(x) = x^2 - 2x - 2 determine the average rate of change of the function over the interval -1 ≤ x ≤ 5

Answer 1

SOLUTION

Given:

Explanation (hint):

$\begin{gathered} f(x)=x^2-2x-2 \\ a=-1 \\ b=5 \end{gathered}$$\begin{gathered} f(a)=f(-1)=(-1)^2-2(-1)-2=1+2-2=1 \\ f(b)=f(5)=5^2-2(5)-2=25-10-2=13 \end{gathered}$$\begin{gathered} The\text{ average rate is:} \\ \frac{f(b)-f(a)}{b-a}=\frac{13-1}{5-(-1)}=\frac{12}{5+1}=\frac{12}{6}=2. \end{gathered}$

The average rate of change of the function is 2.