Respuesta :
ANSWER
[tex]undefined[/tex]EXPLANATION
To find the average rate of change of the function, we have to apply the formula:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]for a ≤ x ≤ b
This implies that:
[tex]\begin{gathered} a=-6 \\ b=2 \end{gathered}[/tex]Therefore, the average rate of change of the function is:
[tex]\frac{f(2)-f(-6)}{2-(-6)}[/tex]To find f(2), we have to substitute 2 for x in the given function:
[tex]\begin{gathered} f(2)=-(2)^2-9(2)+25 \\ f(2)=-4-18+25 \\ f(2)=3 \end{gathered}[/tex]To find f(-6), substitute -6 for x in the given function:
[tex]\begin{gathered} f(-6)=-(-6)^2-9(-6)+25 \\ f(-6)=-36+54+25 \\ f(-6)=43 \end{gathered}[/tex]Therefore, the average rate of change of the function is:
[tex]\begin{gathered} \frac{3-43}{2+6} \\ \Rightarrow\frac{-40}{8} \\ \Rightarrow-5 \end{gathered}[/tex]That is the answer.
