Point of DIminishing returns HELP!!!

[tedog1985]

I need help with this problem. I have no clue how to do it at all.

Find the point of diminishing returns (x,y) = (4/27) (-x^3 + 66x^2 +1050x - 400)

Where 0 less that or equal to x less than or equal to 25

R(x) represents revenue in thousands of dollars, and

x represents the amount spent in advertising in thousands of dollars.

HELP PLEASE !!! Thanks for your time

 

[Gene]

There seems to be something wrong with the problem. There is no deminishing return in that range. The curve increases from x=0 and doesn't start dropping till around x=50.

 

[Razor X]

The problem is fine. Diminishing returns occurs at the inflection point, NOT when the slope of the function changes from positive to negative.

To find the inflection point, find where the second derivative changes from positive to negative.

I graphed the second derivative and verified it crosses the x-axis before x = 25.

 

[Gene]

Ok, I guess I've lost my economics.
-----------------
Gene

 

[Razor X]

haha, no worries, I had the worst teacher for that class. the only reason i remeber was becasue i saw the diminishing returns graph a little after learing about inflection points and connected the two.

 

[tedog1985]

stiil lost!!!!!

 

[Gene]

Razor said take the second derivitive and set it equal to zero. Where are you lost?

 

[tedog1985]

HOw do i find the first derivative of this problem?

 

[Razor X]

Use the power rule.

R(x) = (4/27)(-x^3 + 66x^2 +1050x - 400)
R'(x) = (4/27)(-3x^2 + 132x + 1050)

 

[stapel]

HOw do i find the first derivative of this problem?

Apply the usual derivative rule for polynomial terms: For y = axⁿ, the derivative is y' = anx^n-1.

Eliz.

 

[tedog1985]

Can someone post a step by step for me! Im totaly lost still I keep coming up with the wrong answer and different things. Thanks so much for your time and patience

 

[stapel]

Can someone post a step by step for me!

Most of the tutors don't provide fully-worked solutions. Instead, they try to help the students learn to find the solutions themselves.

I keep coming up with the wrong answer

Please reply showing what you have done, and the tutors will be glad to help you find any errors.

Thank you.

Eliz.

 

[tedog1985]

R(x) = (4/27) (-x^3 + 66x^2 +1050x - 400)

R`(x) = (4/27) (-3x² + 132x +1050)

= -3x² +132x +1050

R``(x) = -3x +132 = 0

-6x = -132

x = 20

The point of diminishing return is at x = 20.

 

[stapel]

R`(x) = (4/27) (-3x² + 132x +1050)

= -3x² +132x +1050

How did you get that (4/27)(-3x² + 132x + 1050) equalled -3x² + 132x + 1050? How did you strip off the leading factor?

R``(x) = -3x +132

The derivative of -3x² is not -3x. Check this step.

Eliz.

 

[tedog1985]

ok this is what im getting now

R(x) = (4/27) (-x^3 + 66x^2 +1050x - 400)

R`(x) = (4/27) (-3x² + 132x +1050)

= -3x² +132x +1050

R``(x) = -6x +132 = 0

-6x = -132

x = 22

Im just looking of an example in the book how to do this. I could not find any rules on this!

 

[tedog1985]

I think i just mis calculated.