Maximizing f(x) = x^2 on the interval [0, a]

[gajanan]

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!

 

[mathman]

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