y = (x-1)*3次根号下x² = (x-1) * x^(2/3) = x^(5/3) - x^(2/3)
y′ = (5/3)x^(2/3) - (2/3)x^(-1/3) = (1/3)x^(-1/3) * (5x-2)
y′′ = (10/9)x^(-1/3) + (2/9)x^(-4/3) = (2/9)x^(-4/3) * (5x+1)
凸区间:(-∞,-1/5)
凹区间:(-1/5,+∞)
x=-1/5时,y= (-1/5-1) * 3次根号下(1/25) = (-6/25)*3次根号下5
拐点:(-1/5,(-6/25)*3次根号下5 )
求二阶导数:
y=(x-1)x^(2/3)
y'=x^(2/3)+(x-1)*2/3x^(-1/3)
y"=