find the average rate of change of $f(x)=x^{2}+4x - 2$ from $x=-8$ to $x=3$
rate of change=

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The formula for 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, $a=-8$, $b = 3$, and $f(x)=x^{2}+4x - 2$.
## Step2: Calculate $f(-8)$
Substitute $x=-8$ into $f(x)$:
$$
\begin{align*}
f(-8)&=(-8)^{2}+4\times(-8)-2\
&=64-32 - 2\
&=30
\end{align*}
$$
## Step3: Calculate $f(3)$
Substitute $x = 3$ into $f(x)$:
$$
\begin{align*}
f(3)&=3^{2}+4\times3-2\
&=9 + 12-2\
&=19
\end{align*}
$$
## Step4: Calculate the average rate of change
Substitute $f(-8) = 30$, $f(3)=19$, $a=-8$, and $b = 3$ into the formula $\frac{f(b)-f(a)}{b - a}$:
$$
\begin{align*}
\frac{f(3)-f(-8)}{3-(-8)}&=\frac{19 - 30}{3 + 8}\
&=\frac{-11}{11}\
&=- 1
\end{align*}
$$

# Answer:
$-1$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(f(-8)\)

Step3: Calculate \(f(3)\)

Step4: Calculate the average rate of change

Answer: