Question

Given the function f(x)=x^2+3x+5, what is the average rate of change of the function between x=1 and x=3?

Answer 1

`\bf slope = \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\leftarrow \begin{array}{llll} \textit{average rate}\\ \textit{of change} \end{array}\\\\ -----------------------------\\\\ f(x)=x^2+3x+5\qquad \begin{cases} x_1=1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(1)}{3-1}`

Answer 2

that's just the slope between the 2 points

evalue f(1) and f(3)
f(1)=1+3+5=9
f(3)=9+9+5=23

slope between (1,9) and (3,23) is
(23-9)/(3-1)=14/2=7

average rate of change is 7