Question

What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)=-2x+1 \qquad \begin{cases} x_1=-5\\ x_2=1 \end{cases}\implies \cfrac{f(1)-f(-5)}{-5-1} \\\\\\ \cfrac{[-2(1)+1]~~-~~[-2(-5)+1]}{-6}\implies \cfrac{[-1]~~-~~[11]}{-6} \\\\\\ \cfrac{-12}{-6}\implies 2$