这道选择题,高数大一 10
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y= (x-1).x^(2/3)
y' =(2/3)(x-1).x^(-1/3) + x^(2/3)
y' =0
(2/3)(x-1).x^(-1/3) + x^(2/3) =0
(1/3)x^(-1/3) . [ 2(x-1) + 3x ] =0
(1/3)x^(-1/3) . (5x-2) =0
x=2/5
y' | x+2/5+ >0
y' | x+2/5- <0
x=2/5 (min)
y(2/5) = (2/5-1).(2/5)^(2/3) = -(3/5)(2/5)^(2/3)
ans : D
y' =(2/3)(x-1).x^(-1/3) + x^(2/3)
y' =0
(2/3)(x-1).x^(-1/3) + x^(2/3) =0
(1/3)x^(-1/3) . [ 2(x-1) + 3x ] =0
(1/3)x^(-1/3) . (5x-2) =0
x=2/5
y' | x+2/5+ >0
y' | x+2/5- <0
x=2/5 (min)
y(2/5) = (2/5-1).(2/5)^(2/3) = -(3/5)(2/5)^(2/3)
ans : D
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