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.

Use the second derivative to justify your answer.

Note: (x>0)

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

Thank you!

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.

Use the second derivative to justify your answer.

Note: (x>0)

Can you differentiate $\displaystyle 2x+100x^{-1}$ twice ?

Re: Having problems finding a value for X using derivatives.

erm,

2x + 100x^-1

2x + 100x^-2 ?

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 $\displaystyle 2-100x^{-2}~\&~200x^{-3}$.

I think you need help that is far beyond what we can give.

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.

Re: Having problems finding a value for X using derivatives.

oh.

how come the 2x changes to just 2?

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?

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

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 ?

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 ?

Re: Having problems finding a value for X using derivatives.

not quite ... the derivative of 2 is 0

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?

Re: Having problems finding a value for X using derivatives.

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 <.<

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?