Question

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -----------------------------\\\\ f(x)=17-x^2\quad \begin{cases} x_1=1\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(1)}{5-1} \\\\\\ \cfrac{(17-5^2)-(17-1^2)}{5-1}\implies \cfrac{-8-16}{4}\implies \cfrac{-24}{4}\implies -6$