曲线Y=(X²-1)(X 1)在X=0处的切线斜率是多少?曲线上那些点的切线平行X轴?
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曲线Y=(X²-1)(X 1)在X=0处的切线斜率是多少?曲线上那些点的切线平行X轴?
曲线Y=(X²-1)(X 1)在X=0处的切线斜率是多少?曲线上那些点的切线平行X轴?
曲线Y=(X²-1)(X 1)在X=0处的切线斜率是多少?曲线上那些点的切线平行X轴?
f(x)=(x²-1)(x+1)
则:
f'(x)=(x²-1)+2x(x+1)
f'(x)=3x²+2x-1
得:
k=f'(0)=-1
切点是P(0,-1)
则切线方程是:x+y+1=0
要使得切线平行x轴,则:k=f'(x)=3x²+2x-1=0
得:x=-1或x=1/3
当切点是M(-1,0)或者N(1/3,-32/27)时,切线与x轴平行.