The monotone increasing interval of function y = (12) - x2 + X + 2 is:___ ．

The monotone increasing interval of function y = (12) - x2 + X + 2 is:___ ．

Let t = - x2 + X + 2 = - (X-2) (x + 1) = - (X-12) 2 + & nbsp; 94,... Y = (12) t, 32 ≥ t ≥ 0, - 1 ≤ x ≤ 2, so the decreasing interval of T is [12,2] and the increasing interval of function y is [12,2]

In which interval does the function f (x) = sin (x + π / 6) + sin (x + π / 3) increase monotonically
A （-π/2,π/12） B （-π/3,π/12） C（π/2,π） D （-2/π,π）

∵ y=sin(x+π/6)+sin(x+π/3)
=sinxcos(π/6)+cosxsin(π/6)+sinxcos(π/3)+cosxsin(π/3)
=(1/2+√3/2)sinx+(1/2+√3/2)cosx
=(1/2+√3/2)*√2[sinx*(√2/2)+cosx*(√2/2)]
=(1/2+√3/2)*√2[sinx*cos(π/4)+cosx*sin(π/4)]
=(1/2+√3/2)*√2sin(x+π/4)
∵ y = SiNx increases over (- π / 2, π / 2)
That y = sin (x + π / 4) increases on (- 3 π / 4, π / 4)
For reference, select B