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Homework Help: Optimization number question

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum.

    2. Relevant equations

    3. The attempt at a solution

    let a,b represent the two non negative numbers
    So, x^2+(30-x)^2=s, where s is the sum of their squares
    After expanding, the derivative is:
    let s'=0, then x=15.
    The interval for possible x values is 0≤x≤30.
    So let us check which value gives a maximum.


    Therefore, the two non-negative numbers are 0 and 30. Is this right? I ask because the solution on a worksheet I have indicates that the two numbers are 15 and 15.
  2. jcsd
  3. Apr 23, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are correct that the maximums occur at the ends. Probably a typo in the problem. Maybe they meant minimum.
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