Analysis: Since the monotone decreasing interval of cosx is [2kπ, π+2kπ], let 2kπ.

The solution is: kπ-π/ 12.

Only when k= 1, the condition is satisfied. The range of the solution is [-π/12,5 π/12], and because X belongs to [0,π].

So [0,5 π/12]

2. The answer is 23/2

Analysis: The equation after moving is: f(x)=sin[w(x+π/6)+π/4+2kπ].

Then π/6*w=-π/ 12+2kπ, so when k= 1, w is at least 23/2.

The answer is 1/2.

F(x) has a maximum value in the interval (π/6, π/2), but there is no minimum value, so we know that these two points must be adjacent and satisfy x+y=π.

(You can see it by drawing a positive selection function diagram), when x=π/6, wx+π/3= π/6w+π/3, and x=π/2,

Wx+π/3=π/2w+π/3, and the two expressions add up to π, w= 1/2.