The average rate of change of a function, g(x), over an interval [a, b] is given by
[tex]Average\ rate\ of\ change= \frac{g(b)-g(a)}{b-a} [/tex]
Thus, the average rate of change of [tex]g(x)=-x^2-4x[/tex] over the interval [tex]6\leq x\leq8[/tex] is given by:
[tex]Average\ rate\ of\ change= \frac{[-(8)^2-4(8)]-[-(6)^2-4(6)]}{8-6} \\ \\ = \frac{(-64-32)-(-36-24)}{2} = \frac{-96-(-60)}{2} = \frac{-96+60}{2} = \frac{-36}{2} \\ \\ -18[/tex]
