analyze the functions d(x) and r(x) to determine which has a greater absolute average rate of change over…

analyze the functions d(x) and r(x) to determine which has a greater absolute average rate of change over the interval x = 2 to x = 5. use the two representations, found below, to compare the two relationships. answer each question based on the given representations. what is the average rate of change from x = 2 to x = 5 for function d(x)? what is the average rate of change from x = 2 to x = 5 for function r(x)? which function has a greater absolute average rate of change over the interval x = 2 to x = 5? d(x) x d(x) -5 184 -4 124 -3 76 0 4 0.5 2.5 2 16 5 124 r(x)

analyze the functions d(x) and r(x) to determine which has a greater absolute average rate of change over the interval x = 2 to x = 5. use the two representations, found below, to compare the two relationships. answer each question based on the given representations. what is the average rate of change from x = 2 to x = 5 for function d(x)? what is the average rate of change from x = 2 to x = 5 for function r(x)? which function has a greater absolute average rate of change over the interval x = 2 to x = 5? d(x) x d(x) -5 184 -4 124 -3 76 0 4 0.5 2.5 2 16 5 124 r(x)

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate average rate of change for $d(x)$

For $d(x)$ with $a = 2$, $b = 5$, $d(2)=16$ and $d(5)=124$. Then the average rate of change is $\frac{d(5)-d(2)}{5 - 2}=\frac{124 - 16}{3}=\frac{108}{3}=36$.

Step3: Calculate average rate of change for $r(x)$

For $r(x)$, when $a = 2$, $r(2)=0$ and when $b = 5$, $r(5)=- 12$. Then the average rate of change is $\frac{r(5)-r(2)}{5 - 2}=\frac{-12-0}{3}=-4$. The absolute value of the average rate of change of $r(x)$ is $|-4| = 4$.

Answer:

The average rate of change for $d(x)$ from $x = 2$ to $x = 5$ is $36$. The average rate of change for $r(x)$ from $x = 2$ to $x = 5$ is $-4$. Function $d(x)$ has a greater absolute average rate of change over the interval $x = 2$ to $x = 5$.