Answer
$x=\displaystyle \frac{1}{4}$
Work Step by Step
$y=f(x)=x-x^{1/2} \\$
$f^{\prime}(x)=1-\displaystyle \frac{1}{2}\cdot x^{-1/2}=1-\frac{1}{2\sqrt{x}} \\$
$f^{\prime}(x)=0$ for ... (solve for x)$\\$
$1-\displaystyle \frac{1}{2\sqrt{x}}=0\ \ \ \ $...$/\times 2\sqrt{x}$
$2\sqrt{x}-1=0\\\\$
$2\sqrt{x}=1\\\\$
$\displaystyle \sqrt{x}=\frac{1}{2}\ \ \ \ $...$/$ square both sides$\\\\$
$x=\displaystyle \frac{1}{4}$
