find the average rate of change of ( k(x)=\frac{14}{x} ) over the interval ( 11,14 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The formula for 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, $a = 11$, $b=14$, and $k(x)=\frac{14}{x}$. So we need to find $k(14)$ and $k(11)$ first.
## Step2: Calculate $k(14)$ and $k(11)$
When $x = 14$, $k(14)=\frac{14}{14}=1$. When $x = 11$, $k(11)=\frac{14}{11}$.
## Step3: Substitute into the average - rate - of - change formula
$$
\begin{align*}
\frac{k(14)-k(11)}{14 - 11}&=\frac{1-\frac{14}{11}}{3}\
&=\frac{\frac{11-14}{11}}{3}\
&=\frac{-\frac{3}{11}}{3}\
&=-\frac{3}{11}\times\frac{1}{3}\
&=-\frac{1}{11}\approx - 0.1
\end{align*}
$$

# Answer:
$-\frac{1}{11}$ (or approximately $-0.1$)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(k(14)\) and \(k(11)\)

Step3: Substitute into the average - rate - of - change formula

Answer: