the function defined in the table below, find the average rate function over the interval 10 ≤ x ≤ 40. x…

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

the function defined in the table below, find the average rate 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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 10$, $b = 40$, $f(a)=f(10) = 55$, and $f(b)=f(40)=49$.

Step2: Substitute values into formula

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

Step3: Simplify the expression

$\frac{49 - 55}{40 - 10}=\frac{-6}{30}=-\frac{1}{5}=- 0.2$.

Answer:

$-0.2$