已知函数f(x)=2sin(wx+φ)(w>0,-π/2

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已知函数f(x)=2sin(wx+φ)(w>0,-π/2
已知函数f(x)=2sin(wx+φ)(w>0,-π/2

已知函数f(x)=2sin(wx+φ)(w>0,-π/2
由已知可得,T/2=7π/8-3π/8=π/2,所以T=π=2π/w,则w=2.
当f(3π/8)=2sin(3π/4+φ)=2,必有f(7π/8)=2sin(7π/4+φ)=-2sin(3π/4+φ)=-2,二式完全等价
因此,只能确实,f(3π/8)=2sin(3π/4+φ)是极值点,但不能确实是最大值还是最小值,
所以得3π/4+φ=kπ±π/2,求得φ=kπ-π/4(两种算法化解后只有这一种结果),k为整数
显然,k=0,φ=-π/4符合题意,
故,求得f(x)=2sin(2x-π/4)

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