what is the average rate of change of the function ( f(x) = 2x^{2}+x + 5 ) over the interval ( -2leq xleq 2 )?
a. -4
b. -1
c. 1
d. 4

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$ and $b = 2$, and $f(x)=2x^{2}+x + 5$.
## Step2: Calculate $f(-2)$
Substitute $x=-2$ into $f(x)$:
$$
\begin{align*}
f(-2)&=2(-2)^{2}+(-2)+5\
&=2\times4-2 + 5\
&=8-2 + 5\
&=11
\end{align*}
$$
## Step3: Calculate $f(2)$
Substitute $x = 2$ into $f(x)$:
$$
\begin{align*}
f(2)&=2(2)^{2}+2+5\
&=2\times4+2 + 5\
&=8+2+5\
&=15
\end{align*}
$$
## Step4: Apply the average rate of change formula
$$
\begin{align*}
\frac{f(2)-f(-2)}{2-(-2)}&=\frac{15 - 11}{2 + 2}\
&=\frac{4}{4}\
&=1
\end{align*}
$$

# Answer:
C. 1

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \(f(-2)\)

Step3: Calculate \(f(2)\)

Step4: Apply the average rate of change formula

Answer: