Find the maximum and minimum value of the function y = - 2Sin (x + π / 6) + 3 in the following interval and the corresponding value of X (1) r, (2) [0, π] (3) [π / 2, π / 2]

Find the maximum and minimum value of the function y = - 2Sin (x + π / 6) + 3 in the following interval and the corresponding value of X (1) r, (2) [0, π] (3) [π / 2, π / 2]

y=-2sin(x+π/6)+3
X belongs to R
So x + π / 6 belongs to R
Max = 5 x + π / 6 = 2K π - π / 2 x = 2K π - 2 π / 3
Minimum = 1 x + π / 6 = 2K π + π / 2 x = 2K π + π / 3
2 x belongs to [0, π]
X + π / 6 belongs to [π / 6,7 π / 6]
Maximum = 4 x + π / 6 = 7 π / 6 x = π
Minimum = 1 x + π / 6 = π / 2 x = π / 3
3 x belongs to [- π / 2, π / 2]
X + π / 6 belongs to [- π / 3,2 π / 3]
Max = 3 + radical 3 x + π / 6 = - π / 3 x = - π / 2
Minimum = 1 x + π / 6 = π / 2 x = π / 3