Question

Help pls !! i need to determine average rate of change of the function over the interval

Answer 1

`\boxed{-2}`

Explanation:

Average rate of change ARC of a function
`\displaystyle f(x)` over the interval
`\displaystyle x = [a, b]` is given by the formula:

`ARC = (f(b) - f(a))/(b - a)`

We are given the function

`f(x) = x^2 - 3x - 5\\` and the given interval is [-2, 3]

`\begin {aligned}\\f(3) &= 3^2 - 3(3) - 5\\&= 9 - 9 - 5\\& = -5\\\\f(-2) & = \left(-2\right)^2-3\left(-2\right)-5\\&=4 + 6 - 5\\&= 5 \end{aligned}`

`ARC = (f(3) - f(-2))/(3 - (-2)) = (-5 - 5)/(3 + 2) = (-10)/(5) = - 2`