find maximum n minimum value

Let f(x)=x+sin2x

1. Find dy/dx=1+2cos2x

2.dy/dx=0 ,which implies x=pi/3 and 2pi/3

3.Second derivative of y at x= pi/3 is -4 sin2pi/3 which  is negative., hence  point of maxima

    Second  derivative of y at x= 2 pi/3  is positive,hence the point of minima

4. Maximum value= pi/3 + sq rt of 3/2

  mininmum value = pi/3 - sr rt of 3/2