Question

question 12 - of 20 step 1 of 1
what is the average rate of change of ( f(x) ) from ( x_1 = 6 ) to ( x_2 = 8 )? please write your answer rounded to the nearest hundredth.
( f(x)=sqrt{7 x - 8} )

Explanation:

Step1: Find \(f(x_1)\) and \(f(x_2)\)

When \(x_1 = 6\), \(f(6)=\sqrt{7\times6 - 8}=\sqrt{42 - 8}=\sqrt{34}\approx5.83\)
When \(x_2 = 8\), \(f(8)=\sqrt{7\times8 - 8}=\sqrt{56 - 8}=\sqrt{48}\approx6.93\)

Step2: Use the average - rate - of - change formula

The average rate of change formula is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\)
Substitute \(x_1 = 6\), \(x_2 = 8\), \(f(6)\approx5.83\), \(f(8)\approx6.93\) into the formula:
\(\frac{f(8)-f(6)}{8 - 6}=\frac{6.93 - 5.83}{2}=\frac{1.1}{2}=0.55\)

Answer:

\(0.55\)