The maximum value of \(f(x) = \sin \left( {x + \frac{\pi }{6}} \right) + \cos \left( {x + \frac{\pi }{6}} \right) \) lies in the interval\(\left[ {0,\frac{\pi }{2}} \right] \) if the value of x is?
1
\(\frac{\pi }{6}\)
2
\(\frac{\pi }{{12}}\)
3
\(\frac{\pi }{3}\)
4
\(\frac{\pi }{4}\)