Question

This app is not working it’s making me so mad

Answer 1

`\text{Average rate of change = -1}`Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ f(x)=-3x^2+5x\text{ } \\ \text{the interval \lbrack}-1,\text{ 3\rbrack} \end{gathered}`

Average rate of change is calculated using the formula:

`\begin{gathered} =\text{ }\frac{f(b)\text{ - f(a)}}{b\text{ - a}} \\ \text{where b = large interval, a = small interval} \\ f(b)\text{ is the value of f(x) when x = b} \\ f(a)\text{ is the value of f(x) when x = a} \end{gathered}`
`\begin{gathered} a\text{ = -1, b = 3} \\ f(a)\text{ =f(-1)= -3}(-1)^2\text{ + 5}(-1) \\ \text{f(-1)= -3(}1)^{}\text{ - 5 = -3 - 5} \\ f(-1)\text{ = -}8 \end{gathered}`
`\begin{gathered} f(b)=f(3)=-3(3)^2\text{ + 5(3)}_{} \\ f(3)\text{ =-3(9) + 15 = -27 + 15} \\ f(3)\text{ = }-12 \end{gathered}`

Substitute the values in the average rate of change:

`\begin{gathered} Average\text{ rate of change }=\text{ }\frac{-12\text{ - (-8)}}{3\text{ }-(-1)} \\ Average\text{ rate of change }=\text{ }\frac{-12\text{ + 8}}{3\text{ + 1}} \\ Average\text{ rate of change }=\text{ }(-4)/(4) \\ Average\text{ rate of change }=\text{ -1} \end{gathered}`