Question

Find the average rate of change of f(x) = - 2x ^ 2 - x from x = 1 to x = 6 . Simplify your answer as much as possible .

Answer 1

The average rate of change of a function in the interval [a,b] is given by:

`(f(b)-f(a))/(b-a)`

In this case we have that a=1 and b=6; plugging these values in the formula above we have:

`\begin{gathered} (-2(6)^2-6-(-2(1)^2-1))/(6-1)=(-2(36)-6-(-2(1)-1))/(5) \\ =(-72-6-(-2-1))/(5) \\ =(-78-(-3))/(5) \\ =(-78+3)/(5) \\ =(-75)/(5) \\ =-15 \end{gathered}`

Therefore, the average rate of change in the interval is -15