9.
The function f is defined by
$$\mathrm { f } ( x ) = \frac { ( x + 5 ) ( x + 1 ) } { ( x + 4 ) } - \ln ( x + 4 ) \quad x \in \mathbb { R } \quad x > k$$
- State the smallest possible value of \(k\).
- Show that
$$\mathrm { f } ^ { \prime } ( x ) = \frac { a x ^ { 2 } + b x + c } { ( x + 4 ) ^ { 2 } }$$
where \(a\), \(b\) and \(c\) are integers to be found.
- Hence show that f is an increasing function.
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