# How do you find the average rate of change of y=x^3+1 from x=1 to x=3?

Sep 19, 2014

$\frac{f \left(x + h\right) - f \left(x\right)}{h} = \frac{f \left(b\right) - f \left(a\right)}{b - a}$, where $a$ is the lower bound and $b$ is the upper bound.

Average rate of change

$s l o p e = \frac{f \left(b\right) - f \left(a\right)}{b - a} = \frac{f \left(3\right) - f \left(1\right)}{3 - 1} = \frac{{\left(3\right)}^{3} + 1 - \left({\left(1\right)}^{3} + 1\right)}{3 - 1} = \frac{\left(27 + 1\right) - \left(1 + 1\right)}{3 - 1} = \frac{28 - 2}{3 - 1} = \frac{26}{2} = 13$

Point: $\left(3 , 28\right)$
Point: $\left(1 , 2\right)$

$y = m x + b$

$2 = 13 \left(1\right) + b$

$2 = 13 + b$

$- 11 = b$

$y = 13 x - 11$, the secant line through the points $\left(3 , 28\right)$ and $\left(1 , 2\right)$.