- 确定曲线的凹凸区间和拐点试确定曲线y=1/(4
- 试确定曲线y=1/(4-2x+x^2)的凹凸区间和拐点.
- 1.
y=1/(4-2x+x^2)=
=1/[(x-1-i√3)(x-1+i√3)]=
=[1/(2i√3),1/(x-1-i√3)-1/(x-1+i√3)].
2.
y"=
=[1/(2i√3),2/(x-1-i√3)^3-2/(x-1+i√3)^3]=
=[1/(i√3)]*
*[(x-1+i√3)^3-(x-1-i√3)^3]/[(x-1-i√3)^3(x-1+i√3)^3]=
=[1/(i√3)]*
*[6(x-1)^2(i√3)+2(i√3)^3]/[(4-2x+x^2)^3]=
=6[x(x-2)]/[(4-2x+x^2)^3].
3.
曲线y=1/(4-2x+x^2)的凹区间=
={x,y"≥0}=(-∞,0]∪[2,+∞),
曲线y=1/(4-2x+x^2)的凸区间=
=[0,2],
曲线y=1/(4-2x+x^2)的拐点=
=(0,1/4),(2,1/4).