Question

hw 6 - average rate of change section 2.1: problem 5 (1 point) determine the average rate of change of the following function between the given values of the variable. $f(x)=x^{4}+2x;$ $x = - 3,x = 2$ 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 $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$, $b = 2$, and $f(x)=x^{4}+2x$.

Step2: Calculate $f(-3)$

Substitute $x=-3$ into $f(x)$: $f(-3)=(-3)^{4}+2\times(-3)=81 - 6=75$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2^{4}+2\times2=16 + 4=20$.

Step4: Calculate the average rate of change

$\frac{f(2)-f(-3)}{2-(-3)}=\frac{20 - 75}{2 + 3}=\frac{-55}{5}=-11$.

Answer:

$-11$