- (a) Express \(2 \cos 3 x - 3 \sin 3 x\) in the form \(R \cos ( 3 x + \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\). Give your answers to 3 significant figures.
$$\mathrm { f } ( x ) = \mathrm { e } ^ { 2 x } \cos 3 x$$
(b) Show that \(\mathrm { f } ^ { \prime } ( x )\) can be written in the form
$$\mathrm { f } ^ { \prime } ( x ) = R \mathrm { e } ^ { 2 x } \cos ( 3 x + \alpha )$$
where \(R\) and \(\alpha\) are the constants found in part (a).
(c) Hence, or otherwise, find the smallest positive value of \(x\) for which the curve with equation \(y = \mathrm { f } ( x )\) has a turning point.