Question

the graph of the function f is given for -3 < x < 6. which of the following statements about the rate of change of f over the interval 2 < x < 6 is true?

Explanation:

Step1: Recall rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, $f(2)=\frac{16}{3}$, and we need to find $f(6)=0$.

Step2: Calculate the rate of change

Substitute the values into the formula: $\frac{f(6)-f(2)}{6 - 2}=\frac{0-\frac{16}{3}}{4}=\frac{-\frac{16}{3}}{4}=-\frac{4}{3}$. Since the rate of change $\frac{f(6)-f(2)}{6 - 2}<0$, the function is decreasing over the interval $2

Answer:

The function $f$ is decreasing over the interval $2 < x<6$.