Question

Find the average rate of change for the given function from x = −1 to x = 2.

Answer 1

Well, if you look at the graph, when x = -1, y or f(x) = 4.

and when x = 2, y = 0.

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=-1\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(-1)}{2-(-1)}\implies \cfrac{0-4}{2+1}\implies \cfrac{-4}{3}$