- (a) By writing \(\sec x\) as \(\frac { 1 } { \cos x }\), show that \(\frac { \mathrm { d } ( \sec x ) } { \mathrm { d } x } = \sec x \tan x\).
Given that \(y = \mathrm { e } ^ { 2 x } \sec 3 x\),
(b) find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
The curve with equation \(y = \mathrm { e } ^ { 2 x } \sec 3 x , - \frac { \pi } { 6 } < x < \frac { \pi } { 6 }\), has a minimum turning point at \(( a , b )\).
(c) Find the values of the constants \(a\) and \(b\), giving your answers to 3 significant figures.