Answer
$15$
Work Step by Step
We are given the function:
$f(x)=x^3+2x+1$
Determine the average rate of change of $f$ from $x_1=1$ to $x_2=3$:
$\dfrac{f(x_2)-f(x_1)}{x_2-x_1}=\dfrac{f(3)-f(1)}{3-1}=\dfrac{[3^3+2(3)+1]-[1^3+2(1)+1]}{2}$
$=\dfrac{34-4}{2}=\dfrac{30}{2}$
$=15$
