函数x/x^2-3x+2的增区间(用导数求解)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/19 12:13:49
函数x/x^2-3x+2的增区间(用导数求解)
y=x/(x^2-3x+2)=x/(x-1)(x-2)
y'=x'/[(x-1)(x-2)]+[x/(x-2)]*[1/(x-1)]'+[x/(x-1)]*[1/(x-2)]'
=1/[(x-1)(x-2)]-[x/(x-2)]*[1/(x-1)^2]-[x/(x-1)]*[1/(x-2)^2]
=1/[(x-1)(x-2)]-x/[(x-2)(x-1)^2]-x/[(x-1)(x-2)^2]
=(x-1)(x-2)/[(x-1)^2(x-2)^2]-x(x-2)/[(x-2)(x-1)^2]-x(x-1)/[(x-1)^2(x-2)^2]
=[(x-1)(x-2)-x(x-2)-x(x-1)]/[(x-1)^2(x-2)^2]
=[(x-1)(x-2)-x(x-2)-x(x-1)]/[(x-1)^2(x-2)^2]
=(2-x^2)/[(x-1)^2(x-2)^2]
令y'=0,则x^2=2 【分母[(x-1)^2(x-2)^2]>0】
y'>0时,增区间为:[-√2,√2]
y'=x'/[(x-1)(x-2)]+[x/(x-2)]*[1/(x-1)]'+[x/(x-1)]*[1/(x-2)]'
=1/[(x-1)(x-2)]-[x/(x-2)]*[1/(x-1)^2]-[x/(x-1)]*[1/(x-2)^2]
=1/[(x-1)(x-2)]-x/[(x-2)(x-1)^2]-x/[(x-1)(x-2)^2]
=(x-1)(x-2)/[(x-1)^2(x-2)^2]-x(x-2)/[(x-2)(x-1)^2]-x(x-1)/[(x-1)^2(x-2)^2]
=[(x-1)(x-2)-x(x-2)-x(x-1)]/[(x-1)^2(x-2)^2]
=[(x-1)(x-2)-x(x-2)-x(x-1)]/[(x-1)^2(x-2)^2]
=(2-x^2)/[(x-1)^2(x-2)^2]
令y'=0,则x^2=2 【分母[(x-1)^2(x-2)^2]>0】
y'>0时,增区间为:[-√2,√2]
函数x/x^2-3x+2的增区间(用导数求解)
用导数求f(x)=(x^2 - 3x/2)e^x为增函数的区间.
求函数f(x)=x^2/3的单调区间,用导数知识.
y=3^x^2-4x-5.求函数的单调区间(用导数)
函数y=根号(x+x^2)的单调区间 ( 用导数.)
求函数f(x)=x^3-3x^2-3x+2的单调区间 用导数求
求下列函数的单调区间 y=x^2+ax(a不等于0) 请用导数知识求解
求f(x)=3x-2/x 在x=1处的导数1.用X=X'处的导数定义直接求解2.先求导函数,再代入求解,
用导数求函数y=-x^3-2x^2-4x+5的单调区间
函数f(x)满足f(2)=3,f(x)的导数小于1,求解不等式f(x平方)
(用导数的方法)1.求函数f(x)=x+(1/x)的单调减区间 2用导数的方法证明函数y=2x-x^2在区间(0,1)上
用导数的方法求下列函数的单调区间 f(x)=x(x-1)(x-2)