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 Pre-Calculus and Calculus
 Finding critical points
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Kevitzinn
Average Member

USA
14 Posts

Posted - 10/19/2007 :  13:53:53  Show Profile  Reply with Quote
So I have, y = x(2-x) and I find the derivative is

y' = (x)/(3(2-x)^(2/3)) + (2-x)

Is there some easy way to find the critical points of that? Thank you very much for your time.
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skeeter
Advanced Member

USA
5634 Posts

Posted - 10/19/2007 :  14:47:03  Show Profile  Reply with Quote
y = x(2 - x)1/3

y' = x*(1/3)(2 - x)-2/3*(-1) + (2 - x)1/3

y' = (2 - x)-2/3[-(x/3) + (2 - x)]

y' = (2 - x)-2/3[2 - (4x/3)]

y' = [2 - (4x/3)]/(2 - x)2/3

you should be able to almost "see" the critical values now.

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Kevitzinn
Average Member

USA
14 Posts

Posted - 10/19/2007 :  16:26:24  Show Profile  Reply with Quote
I see you have the right answer and I appreciate your time very much, but I have just one more question.

You said:

y' = (2 - x)-2/3[-(x/3) + (2 - x)]

What I'm confused about is, how did you do that? If -x/3 is to the first power and and (2-x) is to the (1/3) power, how can you pull it out like that? Thanks.
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Kevitzinn
Average Member

USA
14 Posts

Posted - 10/21/2007 :  23:53:39  Show Profile  Reply with Quote
Ohhhh, that's amazing! Thanks for the help, I would have never thought it could have been pulled out like that! Again, thanks a lot for the help, this site is the best.
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