1.直线y=kx+1与曲线y=x3+bx2+c相切于点M(1,2),则b的值为 (　　)

A.-1　 B.0　 C.1　 D.2

【解析】选A.因为直线y=kx+1与曲线 y=x3+bx2+c相切于点M(1,2),

所以点M(1,2)在直线y=kx+1与曲线y=x3+bx2+c上,直线y=kx+1的斜率为k,曲线y=x3+bx2+c的导数为y'=3x2+2bx,

所以k+1=2,k=1,3+2b=1,b=-1.

2.过函数f(x)=1/3x3-x2图像上一个动点作函数的切线,则切线倾斜角的范围是 (　　)

A.[0"," 3π/4] B.[0"," π/2)∪[3π/4 "," π)

C.[3π/4 "," π) D.(π/2 "," 3π/4]

【解析】选B.设切线倾斜角为α(0≤α<π),斜率为k,则tan α=k=f'(x) =x2-2x=(x-1)2-1≥-1,解得α的范围为[0"," π/2)∪[3π/4 "," π).

3.(2019·榆林模拟)曲线f(x)=x3-1/x(x>0)上一动点P(x0,f(x0))处的切线斜率的最小值为 (　　)

A.√3 B.3 C.2√3 D.6

【解析】选C.f(x)=x3-1/x(x>0)的导数f'(x)=3x2+1/x^2 ,

所以在该曲线上点(x0,f(x0))处切线斜率k=3x_0^2+1/(x_0^2 ),

由函数的定义域知x0>0,