Question 1088220
let f(x) = sin(x+π/6)+cos(x+π÷6)

so f'(x) = cos(x+π/6)-sin(x+π÷6) = 0

          tan(x+π/6) = 1  so x = π÷12

Which is stationary point.

also frontier's poitns are candidate.

f(0) = 1/2 +sqrt(3)/2 = (1+sqrt(3))/2.

f(π÷2) = sin(2π/3)+cos(2π/3) = sqrt(3)/2 -1/2 = (sqrt(3)-1)/2 (min).

f(π÷12) = sin(π/4)+cos(π/4) = sqrt(2)/2+sqrt(2)/2 = sqrt(2) (max).

Max is sqrt(2), Min is (sqrt(3)-1)/2, all this not using 
sinusoid's properties.