Question

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

Answer 1

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 = (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 = (g(8) - g(6))/(8 - 6) = ((-(8^2) - 4*8) - (-(6)^2 - 4*6))/(2) = (-96 - (-60))/(2) = (-36)/(2) = -18`