- The function f, defined for \(x \in \mathbb { R } , x > 0\), is such that
$$\mathrm { f } ^ { \prime } ( x ) = x ^ { 2 } - 2 + \frac { 1 } { x ^ { 2 } }$$
- Find the value of \(\mathrm { f } ^ { \prime \prime } ( x )\) at \(x = 4\).
- Given that \(\mathrm { f } ( 3 ) = 0\), find \(\mathrm { f } ( x )\).
- Prove that f is an increasing function.