for a function to be continous left hand limit must be equal to right hand limit 

  lim ( sin2x) =    lim (ax=b)  =             by this we got =>(root 3)/2 = a(pi/6) +b

x->pi/6-            x->pi/6+

  similarly for f''

  lim (2cos2x) =  lim (a)   =                  by this we get a=1

x->pi/6-            x->pi/6+

hence b= (c) 

if liked then pls approve the answer by clicking yes below

answer will c by just solving it by limit on rhl and lhl

then same for f'' from where you get value of a=1 and from f you will get    aΠ/6+b=(3^1/2)/2

and then equate