这道数学题求解
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y= x-2sinx
y' =1-2cosx
y'=0
1-2cosx =0
cosx =1/2
x=π/3 or 5π/3
y''=2sinx
y''(π/3) >0 (min)
y''(5π/3) <0 ( max)
max y = y(5π/3) = 5π/3 - 2sin(5π/3) = 5π/3 +√3
min y = y(π/3) = π/3 - 2sin(π/3) = π/3 - √3
单调
增加 =[ π/3, 5π/3]
减小 = [ 0, π/3] U[ 5π/3, 2π]
y' =1-2cosx
y'=0
1-2cosx =0
cosx =1/2
x=π/3 or 5π/3
y''=2sinx
y''(π/3) >0 (min)
y''(5π/3) <0 ( max)
max y = y(5π/3) = 5π/3 - 2sin(5π/3) = 5π/3 +√3
min y = y(π/3) = π/3 - 2sin(π/3) = π/3 - √3
单调
增加 =[ π/3, 5π/3]
减小 = [ 0, π/3] U[ 5π/3, 2π]
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