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

analyze the functions c(x) and g(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 c(x)? what is the average rate of change from x = 2 to x = 5 for function g(x)? which function has a greater absolute average rate of change over the interval x = 2 to x = 5? c(x) a cubic function that crosses the y - axis at (0, - 210) and crosses the x - axis at (6,0), (-1.75,0), and (1.25,0). the function has a relative minimum and a relative maximum. the function has a y - value of 180 when x = 2 and a y - value of 405 when x = 5

analyze the functions c(x) and g(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 c(x)? what is the average rate of change from x = 2 to x = 5 for function g(x)? which function has a greater absolute average rate of change over the interval x = 2 to x = 5? c(x) a cubic function that crosses the y - axis at (0, - 210) and crosses the x - axis at (6,0), (-1.75,0), and (1.25,0). the function has a relative minimum and a relative maximum. the function has a y - value of 180 when x = 2 and a y - value of 405 when x = 5

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 of $c(x)$

For $c(x)$, $a = 2$, $b = 5$, $c(2)=180$, $c(5)=405$. Then the average rate of change of $c(x)$ is $\frac{c(5)-c(2)}{5 - 2}=\frac{405 - 180}{3}=\frac{225}{3}=75$.

Step3: Calculate average rate of change of $g(x)$

From the graph of $g(x)$, when $x = 2$, $g(2)=- 10$, when $x = 5$, $g(5)=35$. Then the average rate of change of $g(x)$ is $\frac{g(5)-g(2)}{5 - 2}=\frac{35-(-10)}{3}=\frac{35 + 10}{3}=\frac{45}{3}=15$.

Step4: Compare absolute values

The absolute value of the average rate of change of $c(x)$ is $|75| = 75$, and the absolute value of the average rate of change of $g(x)$ is $|15| = 15$. Since $75>15$, $c(x)$ has a greater absolute average rate of change.

Answer:

What is the average rate of change from $x = 2$ to $x = 5$ for function $c(x)$? $75$ What is the average rate of change from $x = 2$ to $x = 5$ for function $g(x)$? $15$ Which function has a greater absolute average rate of change over the interval $x = 2$ to $x = 5$? $c(x)$