Question

数学大神们，帮个忙！

已知p:函数f(x)=(x-2)e^x(e是自然对数的底数),在(m,2m)上市单调函数;q:"x^2-2x<=0"是“x^2-2mx-3mx^2<=0”的充分不必要条件，若pvq为真，p且q为假，求实数m的取值范围。

Answer 1

2/3<=m<1或m<=-2

Answer 2

p:函数f(x)=(x-2)e^x(e是自然对数的底数),在(m,2m)上是单调函数，

f'(x)=(x-1)e^x,
∴m>=1或m<=1/2.
q:"x^2-2x<=0"是“x^2-2mx-3m^2<=0”的充分不必要条件，(改题了)
<==>{x|0<=x<=2}是{x|-m<=x<=3m}的真子集，
<==>2<=3m,
<==>m>=2/3.
pvq为真，p且q为假，

<==>p真q假，或p假q真，
<==>{"m>=1或m<=1/2",且m<2/3},或{1/2<m<1,且m>=2/3},
<==>m<=1/2,或2/3<=m<1,为所求

追问

亲，我就是对这个答案不满意才提问的，复制答案就不必了