Question

the table gives values for the polynomial function f at selected values of x. what is the average rate of change of f over the closed interval 1,4?

x	f(x)
1	16
2	6
3	0
4	10

(1) the exact numerical value of the correct answer does not always appear among the choices given. when this happens, select from among the choices the number that best approximates the exact numerical value.
(2) unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
(3) angle measures for trigonometric functions are assumed to be in radians. make sure your calculator is in radian mode.

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 4$, $f(1)=16$ and $f(4)=10$.

Step2: Substitute values into formula

$\frac{f(4)-f(1)}{4 - 1}=\frac{10 - 16}{4 - 1}$.

Step3: Simplify the expression

$\frac{10 - 16}{4 - 1}=\frac{-6}{3}=- 2$.

Answer:

$-2$