Question

如题,求函数f(x)=cos^2-cosx-2的单调增区间

Answer 1

复合函数f(y)=y²-y-2, y=cosx

cosx在[0+2kπ,π+2kπ]减,（π+2kπ,2π+2kπ]增

f(y)是典型的二次函数,y定义域[-1,+1],f(y)在[-1,-1/2]减,（-1/2,+1]增

cos(2π/3+2kπ)=cos(4π/3+2kπ)=-1/2,cos(π+2kπ)=-1,cos(0+2kπ)=1

∴x∈(2π/3+2kπ,4π/3+2kπ)时,y∈(-1,-1/2),f(x)减

x∈(－2π/3+2kπ,2π/3+2kπ)时,y∈(-1/2,+1),f(x)增

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画下图就明白,我也不知道数有没错,我没算,方法这样应该没错咯