Question

Calculate the average rate of change for the given function, from x = 2 to x = 7.

x f(x)
-2 0
2 15
7 30




a) negative one third
b) one third
c)−3
d) 3

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}\\\\ -------------------------------\\\\ \begin{array}{ccll} x&f(x)\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ -2&0\\2&15\\7&30 \end{array} \qquad \begin{cases} x_1=2\\ x_2=7 \end{cases}\implies \cfrac{f(7)-f(2)}{7-2}\implies \cfrac{30-15}{5} \\\\\\ \cfrac{15}{5}\implies 3`