Question

Given the function f(x) = x² + 8x + 12, determine the average rate of change of
the function over the interval -10 < x < -2.

Answer 1

The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,

$\dfrac{f(b)-f(a)}{b-a}$

Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is

$\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}$