Question

Which expression below gives the average rate of change of the function g(x)= -x^2 -4x on the interval 6 ≤ x ≤ 8?

Answer 1

The average rate of change of a function, g(x), over an interval [a, b] is given by 

$Average\ rate\ of\ change= \frac{g(b)-g(a)}{b-a}$

Thus, the average rate of change of $g(x)=-x^2-4x$ over the interval $6\leq x\leq8$ is given by:

$Average\ rate\ of\ change= \frac{[-(8)^2-4(8)]-[-(6)^2-4(6)]}{8-6} \\ \\ = \frac{(-64-32)-(-36-24)}{2} = \frac{-96-(-60)}{2} = \frac{-96+60}{2} = \frac{-36}{2} \\ \\ -18$