问题1:已知直线l上动点P及两定点A、B,试求f=|PA|+|PB|的最值.讨论:1.点A、B在直线l的异侧.如图一,当P取AB与l的交点时(这样的P点只有一个),fmin=|AB|;f无最大值.2.点A、B在直线l的同侧.如图二,设A′为A关于l的对称点,当P点为A′B与l的交点时(这样的P点只有一个),fmin|PA|+|PB| Question 1: Knowing the moving point P on the straight line l and the two fixed points A and B, try to find the maximum value of f=|PA|+|PB|. Discussion: 1. The points A and B are on the opposite side of the straight line l. First, when P takes the intersection of AB and l (such a P point has only one), fmin=|AB|;f has no maximum value. 2. Points A and B are on the same side of the straight line l. ’ is the symmetry point of A for l, when P point is the intersection of A’B and l (there is only one P point), fmin|PA|+|PB|