Simple maximization question very confused :s

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    Confused Maximization
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SUMMARY

The function f(x) = x^2 is maximized at the endpoint of the interval defined by the constraint 0 ≤ x ≤ a. The maximum value occurs at x = a, yielding a maximum function value of a^2. The solution can be derived using basic arithmetic principles, specifically that if x > y > 0, then x^2 > y^2. Therefore, the correct answer is that the maximum value is a^2 and the value of x that maximizes the function is a.

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gajanan
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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. I am 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!
 
Mathematics news on Phys.org
Basic arithmetic x > y > 0 => x2 > y2, so the max is at a and the max value is a2.
 

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