Question

find the average rate of change of $k(x)=9sqrt{x}$ over the interval $6,7$. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = k(x)$ over the interval $[a,b]$ is $\frac{k(b)-k(a)}{b - a}$. Here, $a = 6$, $b = 7$, and $k(x)=9\sqrt{x}$.

Step2: Calculate $k(7)$ and $k(6)$

$k(7)=9\sqrt{7}\approx9\times2.646 = 23.814$ and $k(6)=9\sqrt{6}\approx9\times2.449 = 22.041$.

Step3: Compute the average rate of change

$\frac{k(7)-k(6)}{7 - 6}=\frac{9\sqrt{7}-9\sqrt{6}}{1}=9(\sqrt{7}-\sqrt{6})\approx9(2.646 - 2.449)=9\times0.197 = 1.773\approx1.8$.

Answer:

$1.8$