given the function ( f(x)=x^{2}+x - 4 ), determine the average rate of change of the function over the interval ( -6leq xleq4 ).

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-6$ and $b = 4$.
## Step2: Calculate $f(-6)$
Substitute $x=-6$ into $f(x)=x^{2}+x - 4$.
$$
\begin{align*}
f(-6)&=(-6)^{2}+(-6)-4\
&=36-6 - 4\
&=26
\end{align*}
$$
## Step3: Calculate $f(4)$
Substitute $x = 4$ into $f(x)=x^{2}+x - 4$.
$$
\begin{align*}
f(4)&=4^{2}+4-4\
&=16+4 - 4\
&=16
\end{align*}
$$
## Step4: Compute the average rate of change
Substitute $f(-6) = 26$, $f(4)=16$, $a=-6$, and $b = 4$ into the formula $\frac{f(b)-f(a)}{b - a}$.
$$
\begin{align*}
\frac{f(4)-f(-6)}{4-(-6)}&=\frac{16 - 26}{4 + 6}\
&=\frac{-10}{10}\
&=- 1
\end{align*}
$$

# Answer:
$-1$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(f(-6)\)

Step3: Calculate \(f(4)\)

Step4: Compute the average rate of change

Answer: