Question

ПОМОГИТЕ! y=lnx-2x,найти хmax-?

Answer 1

$y=ln x-2x;\ x_{max}-?;\ y'=(ln x-2x)'=(ln x)'-(2x)'=frac{1}{x}-2;\ y'=0=frac{1-2x}{x};\ x=frac12;\ xneq0;\ x<0: x=-1: y'=frac{1+2}{-1}=-3<0;\ 00;\ x>frac12: x=1: y'=frac{1-2cdot1}{1}=1-2=-1<0;\ x_{max}=frac12;\ y_{max}=\lnfrac12-2cdotfrac12=-ln2-1$<frac12:>