Question

$y=\frac{x^2}{2}-\log x$ strictly decreases in the interval

• A. $(0,1)$
• B. $[0,1)$
• C. $[0,1]$
• D. $(0,1]$

Answer 1

The correct option is A $(0,1)$

$y^{\prime }=x-\frac{1}{x}$
$0=x^2-1$
$x=\pm 1$
$y^{\prime }=\frac{x^2-1}{x}$
$x^2-1<0$ when $x\in (-1,1)$
$y^{\prime }<0$ when $x\in (0,1)$