12. if ( f(x)=\frac{1}{x} ), what is the average rate of change over (1,2)?

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b=2$, and $f(x)=\frac{1}{x}$.
## Step2: Calculate $f(1)$ and $f(2)$
When $x = 1$, $f(1)=\frac{1}{1}=1$. When $x = 2$, $f(2)=\frac{1}{2}=0.5$.
## Step3: Substitute into the formula
$$
\begin{align*}
\frac{f(2)-f(1)}{2 - 1}&=\frac{0.5-1}{2 - 1}\
&=\frac{- 0.5}{1}\
&=-0.5
\end{align*}
$$

# Answer:
a. -0.5

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(f(1)\) and \(f(2)\)

Step3: Substitute into the formula

Answer: