Question

determine the average rate of change of the following function between the given values of the variable: $f(x)=x^{4}+x$; $x = - 3$, $x = 2$. average rate of change =

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$, $b = 2$, and $f(x)=x^{4}+x$.

Step2: Calculate $f(-3)$

Substitute $x=-3$ into $f(x)$:

$$
LATEXBLOCK0
$$

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$:

$$
LATEXBLOCK1
$$

Step4: Calculate average rate of change

$$
LATEXBLOCK2
$$

Answer:

$-12$