Given:
[tex]g(x)=x^2+6x+12[/tex]And given interval is
[tex][a,b]=[-3,5][/tex]Required:
To find the average rate of change of the given function over the interval −3≤x≤5.
Explanation:
To calculate the average rate of change between the 2 points use.
[tex]\frac{g(b)-g(a)}{b-a}[/tex]Here,
[tex]\begin{gathered} g(b)=g(5) \\ \\ =5^2+6\times5+12 \\ \\ =25+30+12 \\ \\ =67 \end{gathered}[/tex][tex]\begin{gathered} g(a)=g(-3) \\ \\ =(-3)^2+6(-3)+12 \\ \\ =9-18+12 \\ \\ =3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{g(b)-g(a)}{b-a}=\frac{67-3}{5-(-3)} \\ \\ =\frac{64}{8} \\ \\ =8 \end{gathered}[/tex]Final Answer:
The average rate of change of the function over the interval −3≤x≤5 is 8.
