Suppose $f$ is an increasing real-valued function on [$0, ∞$) with $f(x)> 0$ for all $x$ and let
$g (x) = (1/x)∫_0^xf(u)du$
Then which of the following are true:
1. $g(x) ≤ f(x)$ for all $x∈(0,∞)$
2. $xg(x) ≤ f(x)$ for all $x∈ (0, ∞)$
3. $xg(x) ≥ f(0)$ for all $x∈ (0, ∞)$
4. $yg(y) – xg(x) ≤ (y-x)f(y)$ for all $x < y$.
how should i solve this problem.i am completely stuck on it.