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Category > Calculus Posted 10 Jul 2017 My Price 7.00

the rate of change of the revenue in year 3

f(x) = x3 -3x2 + 4 <------ is the model for revenue function and x represents years, y=f(x) represents revenue in thousands of dollars. Assume the model is valid for the years 0<x<5

 

1.Find the rate of change of the revenue in year 3

[I don't see the 'average' word in here so I'm not sure if I have to find the Af(x) and then the Af'(x) or skip that all and calculate f'(x). I just did all of them.]

 

1.0 - f'(x) = 3x2-6x

1.1 - Af(x) = f(x) / x --------------> x2 - 3x + (4/x)

1.2 - Af'(x) = (fg' - gf')/(g2) ----> 2x - 3 - (4/x2)

 

Find the rate of change of revenue in year 3

1.3 - f'(3) = 3(3)2 - 6(3) = 27 - 18 = 9

1.4 - Af'(x) = 2(3)-3-(4/(3)2) = 6 - 3 - (4/9) = 2.555555555556

 

2. In what years are the rates of change equal to 0?

2.0 - f'(x) = 3x2-6x

0 = 3x2-6x

6x = 3x2

6 = 3x

2 = x -------------> f'(2) = 3(2)2 - 6(2) --------> f'(2) = 12 - 12 = 0

2.1 - Af'(x) = (fg' - gf')/(g2) ----> 2x - 3 - (4/x2)

0 = 2x - 3 - (4/x2)

3 = 2x - (4/x2)

3x = 2x2 - 4 .......................stopping since it feels futile.

 

3. Graph the revenue function and in what x interval is the revenue decreasing and in what interval is the revenue increasing?

 

Answers

SuperTutor
(15)
Status NEW Posted 10 Jul 2017 01:07 AM My Price 7.00

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