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Expert: Steve Holleran - 5/9/2007


Question
Find a positive number such that the sum of this number and its reciprocal is a minimum?

Answer
Hi Terrence,

Let's call the number in question x and the sum S.

Then we have :

 s = x   1/x = x = x^-1

So,  S' = 1 - 1x^-2 = 1 - 1/x^2 = 0

when 1 = 1/x^2 i.e, when x =  /- 1.  We can throw out the -1, since you want a positive number.

So x = 1 is our candidate, lets check it in S'':

S'' = 2x^-3 = 2/ x^3 and S''(1) is positive, so it gives a minimum.  

Hope this helps you out.
Steve

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Steve Holleran

Expertise

I can help with all math questions from basic math to Calculus. Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.

Experience

33 years teaching experience in NJ public schools

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B.S. Mathematics : Wake Forest University 1972 M.S. Mathematics : Monmouth University 1981

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