3.
$$\mathrm { g } ( x ) = 4 x ^ { 3 } + a x ^ { 2 } + 4 x + b$$
where \(a\) and \(b\) are constants.
Given that
- ( \(2 x + 1\) ) is a factor of \(\mathrm { g } ( x )\)
- the curve with equation \(y = \mathrm { g } ( x )\) has a point of inflection at \(x = \frac { 1 } { 6 }\)
- find the value of \(a\) and the value of \(b\)
- Show that there are no stationary points on the curve with equation \(y = \mathrm { g } ( x )\).