Question

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

Answer 1

Answer:

The complete question is:

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

When we have a function f(x), the average rate of change of this function in the interval a < x < b is given by:

$r = \frac{f(b) - f(a)}{b - a}$

Then if we have the function g(x) = -x^2 - 4x

and we want to find the average rate of change in the interval 6 < x < 8 we need to compute:

$r = \frac{g(8) - g(6)}{8 - 6} = \frac{(-(8^2) - 4*8) - (-(6)^2 - 4*6)}{2} = \frac{-96 - (-60)}{2} = \frac{-36}{2} = -18$