f(x)=2sin(2x-pi/6 )单调增区间,F(x)在[0,PI/2]最大最小值
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2sin(2x-pi/6 )单调增区间为2x-π/6∈[2kπ-π/2,2kπ+π/2],k为整数

得到x∈[kπ-π/6,kπ+π/3],k为整数

所以,f(x)=2sin(2x-pi/6 )单调增区间为[kπ-π/6,kπ+π/3],k为整数

当k=0时,f(x)的单调增区间为[-π/6,π/3],

当k=1时,f(x)的单调增区间为[5π/6,4π/3]

可知在[0,PI/2],f(x)在[0,π/3]单调递增,在[π/3,π/2]单调递减

所以,f(x)在x=π/3时,取最大值,f(π/3)=2

f(x)在x=0或x=π/2时将会取到最小值,

x=0,f(0)=-1

x=π/2,f(π/2)=-1

由上可得,f(x)在[0,PI/2]区间上,当x=π/3时,取最大值,为2；

当x=0或x=π/2时,取最小值,为-1

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