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