the number of people at the gym at time $x$ hours is represented by the function $g(x)=-3x^{2}+6x + 2$…

the number of people at the gym at time $x$ hours is represented by the function $g(x)=-3x^{2}+6x + 2$. determine the average rate of change of the number of people at the gym over the interval $1leq xleq3$ and interpret the result. use the drop - down arrows to complete the sentences. the average rate of change of the number of people at the gym over the interval $1leq xleq3$ is. this means that, on average, the number of people at the gym

the number of people at the gym at time $x$ hours is represented by the function $g(x)=-3x^{2}+6x + 2$. determine the average rate of change of the number of people at the gym over the interval $1leq xleq3$ and interpret the result. use the drop - down arrows to complete the sentences. the average rate of change of the number of people at the gym over the interval $1leq xleq3$ is. this means that, on average, the number of people at the gym

Answer

Answer:

-6

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b=3$, and $g(x)=-3x^{2}+6x + 2$.

Step2: Calculate $g(3)$

Substitute $x = 3$ into $g(x)$: $g(3)=-3\times3^{2}+6\times3 + 2=-3\times9 + 18+2=-27+18 + 2=-7$.

Step3: Calculate $g(1)$

Substitute $x = 1$ into $g(x)$: $g(1)=-3\times1^{2}+6\times1+2=-3 + 6+2=5$.

Step4: Calculate average rate of change

$\frac{g(3)-g(1)}{3 - 1}=\frac{-7 - 5}{2}=\frac{-12}{2}=-6$.