Question

Find the average rate of change of f(x) = x°-2x² +3+ 3x from x=1 to x=3.Simplify your answer as much as possible.

Answer 1

The average rate of change for a function f(x) from x=a to x=b is:

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

For the given function:

`f(x)=x^3-2x^2+3x`

Averate rate of change from x=1 to x=3:

`\begin{gathered} (f(3)-f(1))/(3-1)=((3^3-2(3)^2+3(3))-(1^3-2(1)^2+3(1)))/(3-1) \\ \\ =((27-2(9)+9)-(1-2+3))/(2) \\ \\ =((27-18+9)-(2))/(2) \\ \\ =(18-2)/(2) \\ \\ =(16)/(2) \\ \\ =8 \end{gathered}`Then, the averate rate of change for the given function from x=1 to x=3 is 8