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= (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= ([-(8)^2-4(8)]-[-(6)^2-4(6)])/(8-6) \\ \\ = ((-64-32)-(-36-24))/(2) = (-96-(-60))/(2) = (-96+60)/(2) = (-36)/(2) \\ \\ -18`