Question

已知函数f(x)=(a+lnx)除以x(a属于R)若a=4求曲线F(X)在点(e,f(e)处的切线方程2 求f(x)的极

Answer 1

a=4,f(x)=(4+lnx)/x

f(e)=(4+1)/e=5/e

f'(x)=(1/x*x-(4+lnx)*1)/x^2=(-3-lnx)/x^2

f'(e)=-4/e^2

即切线的斜率k=f'(e)=-4/e^2

切线方程是y-5/e=-4/e^2*(x-e)

即是y=-4/e^2 x+8/e