求 y=(ax+b)/(cx+d) 的单调性.

问题描述:

求 y=(ax+b)/(cx+d) 的单调性.

y=(ax+b)/(cx+d)=a/c +(b-ad/c)/(cx+d)
若b-ad/c与c同号,则y在负无穷到-c/d区间和-c/d到正无穷区间都单调递减,若b-ad/c与c异号,则y在负无穷到-c/d区间和-c/d到正无穷区间都单调递增.当然用导数求单调性就更简单了.