Question

f(x) = x³ - 9x
x3
What is the average rate of change of f over the
interval [1, 6]?

Answer 1

$f(1) = 1 {}^{3} - 9(1) = - 8 \\ f(6) = 6 {}^{3} - 9(6) = 162$

$rate = \frac{f(6) - f(1)}{6 - 1} = \frac{162 - ( - 8)}{6 - 1} = \frac{170}{5} \\ rate \: of \: change = 34 \: y \: per \: x$