求下列函数的单调区间.极值点和极值 y=(x-1)^2(x+1)^3
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y = [(x-1)^2](x+1)^3
y' = 3[(x-1)^2](x+1)^2 + [(x+1)^3]2(x-1)
= [(x+1)^2](x-1) ( 3(x-1)+2(x+1))
= [(x+1)^2](x-1)(5x-1)
y'=0
=> x= -1 or 1 or 1/5
x=-1, y = 0
x= 1 , y = 0
x = 1/5, y = (4/5)^2(6/5)^3 = 3456/3125
极值点 = (-1,0) or (1,0) or (1/5,3456/312)
极值 = 3456/3125
y' = 3[(x-1)^2](x+1)^2 + [(x+1)^3]2(x-1)
= [(x+1)^2](x-1) ( 3(x-1)+2(x+1))
= [(x+1)^2](x-1)(5x-1)
y'=0
=> x= -1 or 1 or 1/5
x=-1, y = 0
x= 1 , y = 0
x = 1/5, y = (4/5)^2(6/5)^3 = 3456/3125
极值点 = (-1,0) or (1,0) or (1/5,3456/312)
极值 = 3456/3125
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