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我们知道,数形结合是解决某些函数最值问题的一种基本对策,然而,要确定其一图形的极值状态,探求最值点的位置,往往也并非轻而易举的事,本文主要就直线或圆锥曲线上一点到两定点的距离之和(或差的绝对值)的最值问题,进行分类探讨,给出关于最值点位置的一组命题,并运用这些结论解决一类无理函数的最值问题。 1 曲线C上一点P到两定点A、B的距离之和的最值命题1 若A、B两点在曲线C的异侧,则当P在
We know that combination of number and shape is a basic countermeasure to solve the problem of the most value of some functions. However, to determine the extremum state of a graph, it is not always an easy task to find the position of the most value point. This article mainly focuses on the straight line. Or the maximum value of the sum of the distance (or the absolute value of the difference) from one point to two fixed points on the conic curve, conduct a classification discussion, give a set of propositions about the location of the most value points, and use these conclusions to solve a class of irrational functions. The problem of the highest value. 1 The maximum value of the sum of the distance from the point P on the curve C to the two fixed points A and B. Proposition 1 If the two points A and B are on the opposite side of the curve C, then