20. (03.04 mc) calculate the average rate of change for the function f(x)= - 2x^4+x^3 - 3x^2+x - 4, from x = - 1 to x = 0. (1 point)

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Accepted Answer

# 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, $a=-1$, $b = 0$, and $f(x)=-2x^{4}+x^{3}-3x^{2}+x - 4$.
## Step2: Calculate $f(-1)$
Substitute $x=-1$ into $f(x)$:
$$
\begin{align*}
f(-1)&=-2(-1)^{4}+(-1)^{3}-3(-1)^{2}+(-1)-4\
&=-2\times1 - 1-3\times1 - 1-4\
&=-2-1 - 3-1 - 4\
&=-11
\end{align*}
$$
## Step3: Calculate $f(0)$
Substitute $x = 0$ into $f(x)$:
$$
\begin{align*}
f(0)&=-2(0)^{4}+(0)^{3}-3(0)^{2}+(0)-4\
&=-4
\end{align*}
$$
## Step4: Calculate the average rate of change
$$
\begin{align*}
\frac{f(0)-f(-1)}{0-(-1)}&=\frac{-4-(-11)}{0 + 1}\
&=\frac{-4 + 11}{1}\
&=7
\end{align*}
$$
# Answer:
7

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QUESTION IMAGE

Question

Explanation:

Step1: Recall average rate - of - change formula

Step2: Calculate $f(-1)$

Step3: Calculate $f(0)$

Step4: Calculate the average rate of change

Answer: