Question

1. if ( f(15) = 40 ) and ( f(30) = 22 ), what is the average rate of change on the interval (15, 30)?
2. if ( f(3) = 22 ) and ( f(15) = 34 ), what is the average rate of change on the interval ( 3 leq x leq 15 )?

Explanation:

Step1: Recall average rate formula

The average rate of change of a function $f(x)$ on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Solve Question 8

Substitute $a=15, b=30, f(15)=40, f(30)=22$
$\frac{f(30)-f(15)}{30-15}=\frac{22-40}{30-15}=\frac{-18}{15}=-\frac{6}{5}=-1.2$

Step3: Solve Question 9

Substitute $a=3, b=15, f(3)=22, f(15)=34$
$\frac{f(15)-f(3)}{15-3}=\frac{34-22}{15-3}=\frac{12}{12}=1$

Answer:

1. $-1.2$ (or $-\frac{6}{5}$)
2. $1$