Question

Given the function h(x) = x^2 + 3x - 1 determine the average rate of change of the function over the interval -7 ≤ x ≤ 5

Answer 1

Given:

`x^2+3x-1`

Find: average rate of change of the function over the interval -7 ≤ x ≤ 5

Explanation: the average rate of change of the function is

`\begin{gathered} (f(b)-f(a))/(b-a) \\ \end{gathered}`
`\begin{gathered} f(b)=f(5)=5^2+15-1 \\ =25+15-1 \\ =39 \\ f(a)=f(-7)=(-7)^2-21-1 \\ =49-22 \\ =27 \end{gathered}`
`(f(b)-f(a))/(b-a)=(39-27)/(5-(-7))=(12)/(12)=1`

Final answer: the required answer is 1.