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

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:} \\ (f(b)-f(a))/(b-a)=(13-1)/(5-(-1))=(12)/(5+1)=(12)/(6)=2. \end{gathered}`

The average rate of change of the function is 2.