given the function ( g(x)=x^{2}-5x + 2 ), determine the average rate of change of the function over the interval ( -3leq xleq4 ).

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here $a=-3$ and $b = 4$.
## Step2: Calculate $g(-3)$
Substitute $x=-3$ into $g(x)=x^{2}-5x + 2$.
$$
\begin{align*}
g(-3)&=(-3)^{2}-5\times(-3)+2\
&=9 + 15+2\
&=26
\end{align*}
$$
## Step3: Calculate $g(4)$
Substitute $x = 4$ into $g(x)=x^{2}-5x + 2$.
$$
\begin{align*}
g(4)&=4^{2}-5\times4+2\
&=16-20 + 2\
&=-2
\end{align*}
$$
## Step4: Calculate the average rate of change
Substitute $g(-3)=26$, $g(4)=-2$, $a=-3$ and $b = 4$ into the formula $\frac{g(b)-g(a)}{b - a}$.
$$
\begin{align*}
\frac{g(4)-g(-3)}{4-(-3)}&=\frac{-2-26}{4 + 3}\
&=\frac{-28}{7}\
&=-4
\end{align*}
$$

# Answer:
$-4$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(g(-3)\)

Step3: Calculate \(g(4)\)

Step4: Calculate the average rate of change

Answer: