f(x)=sin²x+根号3sinxcosx+2cos²x,x属于R,求函数f(x)的单调增区间.
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![f(x)=sin²x+根号3sinxcosx+2cos²x,x属于R,求函数f(x)的单调增区间.](/uploads/image/z/625812-60-2.jpg?t=f%28x%29%3Dsin%26%23178%3Bx%2B%E6%A0%B9%E5%8F%B73sinxcosx%2B2cos%26%23178%3Bx%2Cx%E5%B1%9E%E4%BA%8ER%2C%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4.)
f(x)=sin²x+根号3sinxcosx+2cos²x,x属于R,求函数f(x)的单调增区间.
f(x)=sin²x+根号3sinxcosx+2cos²x,x属于R,求函数f(x)的单调增区间.
f(x)=sin²x+根号3sinxcosx+2cos²x,x属于R,求函数f(x)的单调增区间.
f(x)=sin²x+根号3sinxcosx+2cos2x
=(1/2)(1+3cos2x+√3sin2x)
=√3sin(2x+π/3)+1/2
最小正周期为π,增区间由(2k-1/2)π
f(x)=0.5(1-cos2x)+√3sin2x=0.5√3sin2x-0.5cos2x+1/2=sin(2x-π/6)+1/2
∴T=2π/2=π
∵-π/2+2kπ<2x-π/6<π/2+2kπ,(k∈Z)
∴-π/6+kπ
分解 ()*()
在求导:
导数大于0.