Question

函数f(x)=㏑x–ax在点A(2,f(2))处切线L的斜率等于3/2.(1)则求实数a的值?(2)证明,除点A外函数f

Answer 1

(1)

∵f(x)=㏑x–ax

∴f'(x)=1/x-a

∴f'(2)=1/2-a=3/2

∴a=-1

(2)

由(1)可求出直线l方程为y=(3/2)x+ln2-1

构建函数h(x)=(3/2)x+ln2-1-f(x)=-lnx+(1/2)x+ln2-1

h'(x)=-(1/x)+1/2 (由题设知x>0)

∵x>2时h'(x)>0

x=2时h'(x)=0

x