Question

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Find the average rate of change of f(x) over the interval [3, 13].
x 3 4 7 10 13
f(x) 2 8 10 12 22

Answer 1

The average rate of change of $f(x)$ over the interval [3, 13] is given by the ratio

$\dfrac{f(13)-f(3)}{13-3}=\dfrac{22-2}{13-3}=\dfrac{20}{10}=2$