- The function f is defined by
$$f ( x ) = \frac { 2 x - 3 } { x ^ { 2 } + 4 } \quad x \in \mathbb { R }$$
- Show that
$$\mathrm { f } ^ { \prime } ( x ) = \frac { a x ^ { 2 } + b x + c } { \left( x ^ { 2 } + 4 \right) ^ { 2 } }$$
where \(a\), \(b\) and \(c\) are constants to be found.
- Hence, using algebra, find the values of \(x\) for which f is decreasing. You must show each step in your working.