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问题: 设函数F(x)=cos(3x+a-π

解答:

(1) 奇函数--->f(0)=cos(φ-π/6)=0--->φ=2π/3
(2) f(x)=x+cos3x+cos(3x+π/2)
    =x+cos3x-sin3x
    =x+√2cos(3x+π/4)
--->f'(x)=1-3√2sin(3x+π/4)
∵x∈(-π/6,0)--->3x+π/4∈(-π/4,π/4)
--->√2sin(3x+π/4)∈(-1,1)--->斜率f'(x)∈(-2,4)