Question

100 POINTS
What is the average rate of change of the function over the interval x = 0 to x = 8?

f(x)=2x−1/3x+5
Enter your answer, as a fraction, in the box.

Answer 1

Step-by-step explanation:

Step 1:  Find the average rate of change

$ARC = \frac{f(b)-f(a)}{b-a}$

Average Rate of Change is same as ARC

If you mean:  $f(x)=2x - \frac{1}{3}x+5$

$ARC = \frac{f(8)-f(0)}{8-0}$

$ARC=\frac{(2(8)-1/3(8)+5) - (2(0)-1/3(0)+5)}{8}$

$ARC=\frac{(16-8/3+5)-(5)}{8}$

$ARC=\frac{16-8/3}{8}$

$ARC=\frac{40/3}{8}$

$ARC=\frac{5}{3}$

If by the first way, the answer is: The average rate of change is 5/3

If you mean:  $f(x)=\frac{2x - 1}{3x+5}$

$ARC=\frac{f(8)-f(0)}{8-0}$

$ARC=\frac{\frac{2(8)-1}{3(8)+5}-\frac{2(0)-1}{3(0)+5} }{8}$

$ARC=\frac{ \frac{15}{29} - \frac{-1}{5} }{8}$

$ARC=\frac{\frac{ 104 }{ 145 } }{8}$

$ARC=\frac{ 13 }{ 145 }$

If by the second way, the answer is: The average rate of change is 5/3