已知f(x)=2sin(2x+π/6)+a+1(a∈R,a为常数)(1)若x∈R,求f(x)的最小正周期;(2)若f(x)在[-π/6,π/6]上最大值与最小值之和为3,求a的值;(3)求(2)条件下f(x)的单调减区间

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已知f(x)=2sin(2x+π/6)+a+1(a∈R,a为常数)(1)若x∈R,求f(x)的最小正周期;(2)若f(x)在[-π/6,π/6]上最大值与最小值之和为3,求a的值;(3)求(2)条件下f(x)的单调减区间

已知f(x)=2sin(2x+π/6)+a+1(a∈R,a为常数)(1)若x∈R,求f(x)的最小正周期;(2)若f(x)在[-π/6,π/6]上最大值与最小值之和为3,求a的值;(3)求(2)条件下f(x)的单调减区间
已知f(x)=2sin(2x+π/6)+a+1(a∈R,a为常数)
(1)若x∈R,求f(x)的最小正周期;
(2)若f(x)在[-π/6,π/6]上最大值与最小值之和为3,求a的值;
(3)求(2)条件下f(x)的单调减区间

已知f(x)=2sin(2x+π/6)+a+1(a∈R,a为常数)(1)若x∈R,求f(x)的最小正周期;(2)若f(x)在[-π/6,π/6]上最大值与最小值之和为3,求a的值;(3)求(2)条件下f(x)的单调减区间
(1)正周期显然为2π/ω=2π/2=π
(2)单看2sin(2x+π/6)这个函数在[-π/6,π/6]上的极值,解-0.5π

(1)T=2π/2=π
2)当x∈[-π/6,π/6],2x+π/6∈[-π/6,π/2],则当x=-π/6时,f(x)有最小值=a, 当x=π/6时,f(x)有最大值=a+3,所以2a+3=3,则a=0
(3)由(2)得f(x)=2sin(2x+π/6)+1,令2kπ+π/2≤2x+π/6≤2kπ+π/2,的单调减区间为
[kπ+π/6,kπ+2π/3]