So I was given $f(x)$ continuous and positive on $[0,\infty)$, and need to show that $g(x)$ increasing on $(0,\infty)$
And $g(x)={\int_0^xtf(t)dt\over \int_0^xf(t)dt} $
So my approach is I want to show that $g'(x)>0$, so I used FTC and quotient rule to take the derivative of $g'(x)$, but then I got suck at midway because I cannot simplify it.