question given the function defined in the table below, find the average rate of change, in simplest form…

question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 ≤ x ≤ 40. x f(x) 10 55 20 53 30 51 40 49 50 47 60 45

question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 ≤ x ≤ 40. x f(x) 10 55 20 53 30 51 40 49 50 47 60 45

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 10$, $b = 40$, $f(10)=55$, and $f(40)=49$.

Step2: Substitute values into formula

$\frac{f(40)-f(10)}{40 - 10}=\frac{49 - 55}{40 - 10}$.

Step3: Simplify the expression

$\frac{49 - 55}{40 - 10}=\frac{-6}{30}=-\frac{1}{5}$.

Answer:

$-\frac{1}{5}$