f′(x)=a+1/x=(ax+1)/x,令f′(x)=0,则x=-1/a
(1)当a≧0时,
当x＜-1/a,f′(x)﹤0,f(x)为减函数；当x≧-1/a,f′(x)＞0,f(x)为增函数,故x=-1/a,f(x)为极小值.
而f(1)=a,则f(e)=ae+1为极大值,
（2）当a＜0时
x＜-1/a,f′(x)＞0,f(x)为增函数；当x≧-1/a,f′(x)＜0,f(x)为减函数,则,极大值为f(-1/a)=-1-ln(-a)