Expert: Paul Klarreich - 8/15/2009

Question
Hi Mr. Klarreich
Regarding the question that was posted on a max and min problem, i am slightly confused as to how a function was reached

http://en.allexperts.com/q/Calculus-2063/2008/12/Min-Max-problem-5.htm

the series of events were as such:
1) D^2 = x^2 - 2x + 1 + y^2     - 6  y            + 9

2) D^2 = x^2 - 2x + 1 + x^2 - 4 - 6 sqrt(x^2 - 4) + 9

3) D^2 = 2x^2 - 2x  + sqrt(x^2 - 4)
I'm not sure if there is a slight algebra mistake from step 2 to 3, maybe I cannot see something, but if one has

D^2 = x^2 - 2x + 1 + x^2 - 4 - 6 sqrt(x^2 - 4) + 9

does it not simplify to 2x^2 - 2x -6sqrt(x^2-4) + 6
and then the derivative is
4x -2 -6x/ (sqrt (x^2-4)?? where does the 6 coefficent go? (i understand that the constant is irrelevant)

If there is an algebra mistake on my part could you please show it to me? sorry for bringing up a math ghost's past.

If this is a correction, then I'm sure its just its just a slight mistake in the expansive help that you provide us in calc need, and i'd like to thank you, and this forum, hopefully it will help me pass my final :D.  

Answer
Questioner: hindude
Country: United States
Category: Calculus
Private: No
Subject: Max Min problem correction
Question: Hi Mr. Klarreich
Regarding the question that was posted on a max and min problem, i am slightly confused as to how a function was reached

http://en.allexperts.com/q/Calculus-2063/2008/12/Min-Max-problem-5.htm

the series of events were as such:
1) D^2 = x^2 - 2x + 1 + y^2     - 6  y            + 9

2) D^2 = x^2 - 2x + 1 + x^2 - 4 - 6 sqrt(x^2 - 4) + 9

3) D^2 = 2x^2 - 2x  + sqrt(x^2 - 4)
I'm not sure if there is a slight algebra mistake from step 2 to 3, maybe I cannot see something, but if one has

D^2 = x^2 - 2x + 1 + x^2 - 4 - 6 sqrt(x^2 - 4) + 9

does it not simplify to 2x^2 - 2x -6sqrt(x^2-4) + 6
and then the derivative is
4x -2 -6x/ (sqrt (x^2-4)?? where does the 6 coefficent go? (i understand that the constant is irrelevant)

If there is an algebra mistake on my part could you please show it to me? sorry for bringing up a math ghost's past.

If this is a correction, then I'm sure its just its just a slight mistake in the expansive help that you provide us in calc need, and i'd like to thank you, and this forum, hopefully it will help me pass my final :D.
...........................................
Hi, Hindude,  (I can't imagine your mother actually giving you a name like that.)

I am going to take a further look at this.  I appear to have messed up the algebra very nicely and I'll redo it as soon as I can.  

Thank you for pointing it out.  I generally assume that questioners are in a hurry to get their answers and so I sometimes get careless.

Your "there is a slight algebra mistake from step 2 to 3" is very generous -- I would have some nastier comment.