find the average rate of change of ( k(x)=\frac{14}{x} ) over the interval ( 11,14 ).\nwrite your answer as…

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))