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The diagram shows the curve \(y = \frac { 2 x + 4 } { x ^ { 2 } + 5 }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and hence find the coordinates of the two stationary points.
- The function g is defined for all real values of \(x\) by
$$\mathrm { g } ( x ) = \left| \frac { 2 x + 4 } { x ^ { 2 } + 5 } \right| .$$
(a) Sketch the curve \(y = \mathrm { g } ( x )\) and state the range of g .
(b) It is given that the equation \(\mathrm { g } ( x ) = k\), where \(k\) is a constant, has exactly two distinct real roots. Write down the set of possible values of \(k\).