Question

Find the average rate of change of the function

Answer 1

X1 = 4 so sqrt(4) = 2
x2 = 9 so sqrt(9) = 3
3-2 = 1

9-4 = 5

rate of change = 1/5

Answer 2

To the risk of being redundant

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= \sqrt{x} \qquad \begin{cases} x_1=4\\ x_2=9 \end{cases}\implies \cfrac{f(9)-f(4)}{9-4}\implies \cfrac{\sqrt{9}-\sqrt{4}}{5} \\\\\\ \cfrac{3-2}{5}\implies \cfrac{1}{5}$