Question

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

Answer: 13/145

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Work Shown:

Plug in x = 0

`f(x) = (2x-1)/(3x+5)\\\\f(0) = (2*0-1)/(3*0+5)\\\\f(0) = (0-1)/(0+5)\\\\f(0) = -(1)/(5)\\\\`

Repeat for x = 8

`f(x) = (2x-1)/(3x+5)\\\\f(8) = (2*8-1)/(3*8+5)\\\\f(8) = (16-1)/(24+5)\\\\f(8) = (15)/(29)\\\\`

Now use the average rate of change formula

`m = (f(b)-f(a))/(b-a)\\\\m = (f(8)-f(0))/(8-0)\\\\m = (15/29 - (-1/5))/(8)\\\\m = (15/29 + 1/5)/(8)\\\\m = ((15/29)*(5/5) + (1/5)*(29/29))/(8)\\\\m = (75/145 + 29/145)/(8)\\\\`

`m=(104/145)/(8)\\\\m = (104)/(145) / (8)/(1)\\\\m = (104)/(145) * (1)/(8)\\\\m = (104*1)/(145*8)\\\\m = (104)/(1160)\\\\m = (13)/(145)\\\\`