Answer:
[tex]g_{avg}'(x)=1[/tex]
Step-by-step explanation:
Formula for the average rate of change is
[tex]f_{avg}'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
where [a, b] is your interval and f(x) is your function.
You're given the interval [-2, 4] and the function g(x), so you're average rate of change equation will now be
[tex]g_{avg}'(x)=\frac{g(b)-g(a)}{b-a}[/tex]
[tex]g_{avg}'(x)=\frac{g(4)-g(-2)}{(4)-(-2)}[/tex]
[tex]g_{avg}'(x)=\frac{[\frac{(4)^2}{2}+7]-[\frac{(-2)^2}{2}+7]}{(4)-(-2)}[/tex]
[tex]g_{avg}'(x)=\frac{[15]-[9]}{6}[/tex]
[tex]g_{avg}'(x)=\frac{6}{6}[/tex]
[tex]g_{avg}'(x)=1[/tex]
