Question

What is the average rate of change for the function f(x)=x^3-6x^2+4x+7 over the interval 0

Answer 1

-1

Step-by-step explanation:

Given the function:

`f\mleft(x\mright)=x^3-6x^2+4x+7`

The average rate of change over the interval 0≤x≤5:

`\begin{gathered} \text{Rat of change=}(f(5)-f(0))/(5-0) \\ =((5^3-6(5)^2+4(5)+7)-(0^3-6(0)^2+4(0)+7))/(5) \\ =((125-150+20+7)-(7))/(5) \\ =(2-7)/(5) \\ =-(5)/(5) \\ =-1 \end{gathered}`

The average rate of change for the function over the given interval is -1.