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Simple maximization question! very confused :s

  1. Feb 7, 2012 #1
    Hey everybody!

    My question is: Find the value of x that maximizes the following function and the maximum
    value (a is constant): f(x) = x^2 subject to 0 ≤ x ≤ a.

    It is supposed to be solved without calculus and I'm terrible confused! how would i go about solving this? wen i plot the curve i of course get half a parabola (positive half), and given the constraint 0 ≤ x ≤ a, the graph gets limited. Im confused what the answer to this question would be :s! would it be a^2 as the maximum value and a as the value of x that maximizes the function, or would it simply be 0 or not possible?!? any help would be appreciated greatly!
     
  2. jcsd
  3. Feb 7, 2012 #2

    mathman

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    Science Advisor
    Gold Member

    Basic arithmetic x > y > 0 => x2 > y2, so the max is at a and the max value is a2.
     
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