find the average rate of change of ( h(x)=-x^{3}+11 x^{2}+10 ) over the interval ( 3,11 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 3$, $b=11$, and $f(x)=-x^{3}+11x^{2}+10$.
## Step2: Calculate $f(3)$
Substitute $x = 3$ into $f(x)$:
$$
\begin{align*}
f(3)&=-(3)^{3}+11(3)^{2}+10\
&=-27 + 99+10\
&=82
\end{align*}
$$
## Step3: Calculate $f(11)$
Substitute $x = 11$ into $f(x)$:
$$
\begin{align*}
f(11)&=-(11)^{3}+11(11)^{2}+10\
&=-1331+1331 + 10\
&=10
\end{align*}
$$
## Step4: Apply the average rate of change formula
$$
\begin{align*}
\frac{f(11)-f(3)}{11 - 3}&=\frac{10-82}{8}\
&=\frac{-72}{8}\
&=- 9
\end{align*}
$$

# Answer:
$-9$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \(f(3)\)

Step3: Calculate \(f(11)\)

Step4: Apply the average rate of change formula

Answer: