Question

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

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ between $x = a$ and $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 2$, and $f(x)=x^{4}+2x$.

Step2: Calculate $f(-1)$

Substitute $x=-1$ into $f(x)$: $f(-1)=(-1)^{4}+2\times(-1)=1 - 2=-1$.

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

Use the formula $\frac{f(2)-f(-1)}{2-(-1)}$. Substitute $f(-1)=-1$ and $f(2)=20$: $\frac{20-(-1)}{2 + 1}=\frac{20 + 1}{3}=\frac{21}{3}=7$.

Answer:

7