f(x)=1+2sin x+3cos ²x[0,2p÷3) find max value of function

differentiate the equation and equate it to zero to find the critical points. we get f`(x) = 0 at x=pi/2 or sin^-1(1/6). use the second order derivative test to see which is maxima. [ if f``(x) is -ve it is maxima] we get the maxima at x= sin^-1(1/6) and the value is ------->>> 51/12