7. The curve \(y = a x ^ { 4 } + b x ^ { 3 } + 18 x ^ { 2 }\) has a point of inflection at \(( 1,11 )\).
- Show that \(2 a + b + 6 = 0\).
- Find the values of the constants \(a\) and \(b\) and show that the curve has another point of inflection at \(( 3,27 )\).
- Sketch the curve, identifying all the stationary points including their nature.