Question

Find the points of maximum and minimum and the intervals of monotonicity of the following function:
$y=x-lnx$

Answer 1

$y=x-\ln x$

$\frac{dy}{dx}=1-\frac{1}{x}=0\Rightarrow x=1$

$\frac{d^{2}y}{d{x}^2}=\frac{1}{x^2}>0$

Hence the given function increases continously from $x=1to\infty$,The function y increases monotonically in interval $(1,\infty )$ and has minimum at $x=1$