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Absolute Minimum and Maximum Word Problem

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Find a number in the closed interval [1/2, 3/2] such that the sum of the number and its reciprocal is
    (a)as small as possible
    (b) as large as possible

    I am given the answer in the back of the book
    The answer to a is 1
    The answer to be is 1/2

    2. Relevant equations
    Here is my equation

    S= x + 1/x

    dS/dx = 1-1/x^2

    3. The attempt at a solution
    I was wondering if i should set the derivative equal to zero and find the zeroes for the derivatives???
  2. jcsd
  3. Oct 26, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Absolutely, you should do that. That will give the locations of the local extrema. And don't forget to check the endpoints as well.
    Last edited: Oct 26, 2008
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