Question

函数在区间内的增减性比如,y=根号2倍sin（2x+π/4） 在【-π/4,π/4】内哪个区间是增函数,哪个区间减函数?

Answer 1

结论：在【-π/4,π/8】上是增函数,在【π/8,π/4】上是减函数

-π/4<=x<=π/4时,.-π/4<=2x+π/4<=3π/4

x在单增区间上:-π/4<=2x+π/4<=π/2,解得 -π/4<=x<=π/8

x在单减区间上:π/2<=2x+π/4<=3π/4,解得 π/8<=x<=π/4

3.由(2)得原函数在【-π/4,π/8】上是增函数,在【π/8,π/4】上是减函数

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