- Express \(\frac { 3 } { x ^ { 2 } + 2 x } + \frac { x - 4 } { x ^ { 2 } - 4 }\) as a single fraction in its simplest form.
- The function f , defined for \(x \in ^ { \circ } , x > 0\), 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.