1.设动直线x=m与函数f(x)=x3,g(x)=ln x的图像分别交于点M,N,则|MN|的最小值为 (　　)

A.1/3(1+ln 3) B.1/3ln 3

C.1+ln 3 D.ln 3-1

【解析】选A.设F(x)=f(x)-g(x)=x3-ln x,求导得:F'(x)=3x2-1/x.

令F'(x)>0得x>1/∛3;令F'(x)<0得0

所以当x=1/∛3时,F(x)有最小值为F(1/∛3)=1/3+1/3ln 3=1/3(1+ln 3).

2.若函数f(x)=e-x+tln x有两个极值点,则实数t的取值范围是 (　　)

A.(0"," 1/e) B.("-∞," 1/e)

C.("-" 1/e "," 0) D.(1/e "," +"∞" )

【解析】选A.f'(x)=-e-x+t/x=0有两个正根,即t=xe-x有两个正根,令g(x)=xe-x,

g'(x)=e-x-xe-x,当g'(x)>0时,x<1,故y=g(x)在(0,1)上单调递增,在(1,+∞)上单调递减,g(x)max=g(1)=1/e,当x→+∞时,g(x)>0,所以t∈(0"," 1/e).

3.(2019·南充模拟)若函数f(x)=x3+x2-ax-4在区间(-1,1)内恰有一个极值点,则实数a的取值范围为 (　　)

A.(1,5)

B.[1,5)

C.(1,5]

D.(-∞,1)∪(5,+∞)