已知函数y=x2与y=lnx,则在区间(0,+∞)上增长较快的是?why

If y1=x^2, y2=lnx

then y1'=2x, y2'=1/x

let 2x=1/x

solve this equation, we get x=Sqr(2)/2

if 0<x<Sqr(2)/2，0<y1'<y2',

then y2 grows faster

if x=Sqr(2), y1'=y2'

then both y1 and y2 grow at an equal speed

if x>Sqr(2), y1'>y2'

then y1 grows faster than y2