7. The curve \(C\) has equation \(y = \frac { x } { 4 + x ^ { 2 } }\).
- Use calculus to find the coordinates of the turning points of \(C\).
Using the result \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = \frac { 2 x \left( x ^ { 2 } - 12 \right) } { \left( 4 + x ^ { 2 } \right) ^ { 3 } }\), or otherwise,
- determine the nature of each of the turning points.
- Sketch the curve \(C\).