what is the average rate of change for the function f(x)=3x^2 - 5 on the interval -3≤x≤1? write the average rate of change in the box.

Question

Accepted Answer

# Explanation:
## Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$, $b = 1$, and $f(x)=3x^{2}-5$.
## Step2: Calculate $f(a)$ and $f(b)$
First, find $f(-3)$:
$$
\begin{align*}
f(-3)&=3\times(-3)^{2}-5\
&=3\times9 - 5\
&=27-5\
&=22
\end{align*}
$$
Then, find $f(1)$:
$$
\begin{align*}
f(1)&=3\times1^{2}-5\
&=3 - 5\
&=-2
\end{align*}
$$
## Step3: Calculate the average rate of change
$$
\begin{align*}
\frac{f(1)-f(-3)}{1-(-3)}&=\frac{-2 - 22}{1 + 3}\
&=\frac{-24}{4}\
&=-6
\end{align*}
$$
# Answer:
$-6$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall average - rate - of - change formula

Step2: Calculate $f(a)$ and $f(b)$

Step3: Calculate the average rate of change

Answer: