1.求f(x)=CosX+Cos(x+兀/3)的最值2.X属于[-兀/2,兀/2]求f(X)=SinX+根号Cosx的最值
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![1.求f(x)=CosX+Cos(x+兀/3)的最值2.X属于[-兀/2,兀/2]求f(X)=SinX+根号Cosx的最值](/uploads/image/z/14441146-34-6.jpg?t=1.%E6%B1%82f%28x%29%3DCosX%2BCos%28x%2B%E5%85%80%2F3%29%E7%9A%84%E6%9C%80%E5%80%BC2.X%E5%B1%9E%E4%BA%8E%5B-%E5%85%80%2F2%2C%E5%85%80%2F2%5D%E6%B1%82f%28X%29%3DSinX%2B%E6%A0%B9%E5%8F%B7Cosx%E7%9A%84%E6%9C%80%E5%80%BC)
1.求f(x)=CosX+Cos(x+兀/3)的最值2.X属于[-兀/2,兀/2]求f(X)=SinX+根号Cosx的最值
1.求f(x)=CosX+Cos(x+兀/3)的最值2.X属于[-兀/2,兀/2]
求f(X)=SinX+根号Cosx的最值
1.求f(x)=CosX+Cos(x+兀/3)的最值2.X属于[-兀/2,兀/2]求f(X)=SinX+根号Cosx的最值
f(x)=CosX+Cos(x+兀/3)
=cosx+cosxcosπ/3-sinxsinπ/3
=3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx)
=√3cos(x+π/6)
最大值为√3,最小值为-√3
(2)
f(X)=SinX+根号Cosx
=2(1/2sinx+√3/2cosx)
=2sin(x+π/3)
∵x∈[-π/2,π/2]
∴x+π/3∈[-π/6,5π/6]
∴sin(x+π/3)∈[-1/2,1]
∴2sin(x+π/3)∈[-1,2]
即函数最大值为2,最小值-1
f(x)=cosx+(cosxcosπ/3-sinxsinπ/3)
=cosx+(cosx*1/2-sinx*√3/2)
=cosx*3/2-sinx*√3/2
=√3(cosx*√3/2-sinx*1/2)
=√3(cosxcosπ/6-sinxsinπ/6)
=√3cos(x+π/6)
max f(x)=√3,min f(x)=√-3
f...
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f(x)=cosx+(cosxcosπ/3-sinxsinπ/3)
=cosx+(cosx*1/2-sinx*√3/2)
=cosx*3/2-sinx*√3/2
=√3(cosx*√3/2-sinx*1/2)
=√3(cosxcosπ/6-sinxsinπ/6)
=√3cos(x+π/6)
max f(x)=√3,min f(x)=√-3
f(X)=SinX+根号Cosx
当X属于[-兀/2,0],可由图知两个都是上升的,所以X=0时最大为1+0=1,且最小值为-1
当X属于[0,兀/2],使t=√cos
f(x)=1-t^4-t
求导可得1-4t^3,极点是t³=¼,最高点
f(x)=1-t^4-t=1+t(1-t³)=1+3/2=5/2
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f(x)=CosX+Cos(x+兀/3)
=cosx+cosxcosπ/3-sinxsinπ/3
=3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx)
=√3cos(x+π/6)
最大值为√3,最小值为-√3
(2)
f(X)=SinX+根号Cosx
=2(1/2sin...
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f(x)=CosX+Cos(x+兀/3)
=cosx+cosxcosπ/3-sinxsinπ/3
=3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx)
=√3cos(x+π/6)
最大值为√3,最小值为-√3
(2)
f(X)=SinX+根号Cosx
=2(1/2sinx+√3/2cosx)
=2sin(x+π/3)
∵x∈[-π/2,π/2]
∴x+π/3∈[-π/6,5π/6]
∴sin(x+π/3)∈[-1/2,1]
∴2sin(x+π/3)∈[-1,2]
即函数最大值为2,最小值-1
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