Functional

By completing the square, we have that $y = -(x - \sqrt{x}) = -\left(\sqrt{x} - \dfrac{1}{2}\right)^{2} + \dfrac{1}{4}$ ,

which describes a parabola opening downward with a maximum of $\dfrac{1}{4} = \boxed{0.25}$ at $\sqrt{x} = \dfrac{1}{2} \Longrightarrow x = \dfrac{1}{4}$ .

Taking the derivative, there is a maximum at $x = 0.25$

Substituting that value of $x$ , we get $y = 0.5- 0.25= 0.25$