从图像可知
A=2
周期T=8
∴2π/w=8
w=π/4
f(x)=2sin(π/4x+φ)
f(1)=2sin(π/4+φ)=2
sin(π/4+φ)=1
π/4+φ=π/2+2kπ,k∈Z
φ=π/4+2kπ,k∈Z
∵|φ|<π/2
∴φ=π/4
f(x)=2sin(π/4x+π/4)
(2)
f(x)+f(x+2)
=2sin(π/4x+π/4)+2sin(π/4(x+2)+π/4)
=2sin(π/4x+π/4)+2cos(π/4x+π/4)
=2√2sin(π/4x+π/4+π/4)
=2√2cosπ/4x
x∈[-6.-2/3]
π/4x∈[-3π/2,-π/6]
cosπ/4x∈[-1,√3/2]
2√2cosπ/4x∈[-2√2,√6]
最大值=√6,x=-4
最小值=-2√2,x=-2/3
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