# Having problems finding a value for X using derivatives.

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• Nov 24th 2012, 08:07 AM
agehayoshina
Having problems finding a value for X using derivatives.
Hi,
I am really struggling with these types of questions. So if you've got the time, a way to solve these types of questions in general would be really helpful!

Right, the specific question goes as follows:

Given that P = 2x + 100/x
Find the value of x for which P is minimum.
Note: (x>0)

I have no clue how to go about doing this, let alone what a second derivative is.

Thank you!
• Nov 24th 2012, 08:15 AM
Plato
Re: Having problems finding a value for X using derivatives.
Quote:

Originally Posted by agehayoshina
Given that P = 2x + 100/x
Find the value of x for which P is minimum.
Note: (x>0)

Can you differentiate $2x+100x^{-1}$ twice ?
• Nov 24th 2012, 08:21 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
erm,
2x + 100x^-1
2x + 100x^-2 ?
• Nov 24th 2012, 08:25 AM
Plato
Re: Having problems finding a value for X using derivatives.
Quote:

Originally Posted by agehayoshina
erm,
2x + 100x^-1
2x + 100x^-2 ?

N0! It is $2-100x^{-2}~\&~200x^{-3}$.

I think you need help that is far beyond what we can give.
• Nov 24th 2012, 08:36 AM
skeeter
Re: Having problems finding a value for X using derivatives.
Quote:

Originally Posted by agehayoshina
I have no clue how to go about doing this, let alone what a second derivative is.

If you do not know how to find a minimum or what a second derivative is, then you should not have been assigned this problem. You need a face-to-face talk with your instructor.
• Nov 24th 2012, 08:41 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
oh.

how come the 2x changes to just 2?
• Nov 24th 2012, 08:45 AM
skeeter
Re: Having problems finding a value for X using derivatives.
Quote:

Originally Posted by agehayoshina
oh.

how come the 2x changes to just 2?

do you know what a derivative is? how to find it? what it tells you?
• Nov 24th 2012, 08:48 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
As far as I understand it the derivative of 2x^2 would be 4x^1 so just 4x. Is that correct or am I totally wrong on this?

thanks
• Nov 24th 2012, 08:50 AM
skeeter
Re: Having problems finding a value for X using derivatives.
that's fine ... but why do you not understand that the derivative of 2x is 2 ?
• Nov 24th 2012, 08:56 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
OH! i see. So would the derivatives of 2x+100x^-1 be

2 - 100x^-2

and

2 + 200x^-3 ?
• Nov 24th 2012, 09:01 AM
skeeter
Re: Having problems finding a value for X using derivatives.
not quite ... the derivative of 2 is 0
• Nov 24th 2012, 09:04 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
okay. so just 200x^-3? ..also how can i use this to prove/find the minimum value of x for P?
• Nov 24th 2012, 09:10 AM
skeeter
Re: Having problems finding a value for X using derivatives.
• Nov 24th 2012, 09:18 AM
Petrus
Re: Having problems finding a value for X using derivatives.
when u find a max and min point u derivate and set to zero then u put it on second derivate and se if its possitive i think its a min point and if its negative its max. wait for some1 to confirme im kinda tired so i can write wrong <.<
• Nov 24th 2012, 09:32 AM
agehayoshina
Re: Having problems finding a value for X using derivatives.
Thanks @skeeter ! how would i apply this to the top question. I am mostly cleared up on the derivative area...but how do i find the minimum which they're asking for in the question?
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