+9575 Let \(t = \sqrt x\).
\(t^2 = x\)
So the objective function is just \(t - t^2\).
Completing the square yields \(t - t^2 = \dfrac14 - \left(t - \dfrac12\right)^2\)
So, when \(t = \dfrac12\), the maximum value of the objective function is attained, and the value is \(\boxed{\dfrac14}\)
