Question

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

Answer 1

`-1`

Step-by-step explanation

Given;

`\begin{gathered} f(x)=x^2-5x-2 \\ (-1,5) \end{gathered}`
`\begin{gathered} f(-1)=(-1)^2-5(-1)-2 \\ =1+5-2 \\ =4 \end{gathered}`

For x = 5;

`\begin{gathered} f(5)=(5)^2-5(5)-2 \\ =25-25-2 \\ =-2 \end{gathered}`

The average is calculated using;

`\begin{gathered} (f(-1)-f(5))/(-1-5) \\ =(4-(-2))/(-1-5) \\ =(6)/(-6) \\ =-1 \end{gathered}`

A