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极大与极小問題是有很大实际应用意义的,因而人們对它有相当浓厚的兴趣,微分学給出了解决这一类問題的一般方法。但讀者要注意,有些問題利用初等数学的知識来解决往往更簡单更敏捷更巧妙。下面我們就准备用初等数学的方法来解决一些物理学中的极大与极小問題。 1.将一物体以初速v_0垂直向上抛出,問此物体的最高点在何处?何时到达? 解。设最高点与地面的距离为h,此物体經过t秒钟到达最高点。由于地球引力的作用,垂直向上拋出的物体作匀减速运动。显然物体在最高点的速度等于零。所以
The maximum and minimum problems are of great practical significance. Therefore, people have a very strong interest in it. Differential calculus gives a general method to solve this type of problem. But readers should be aware that there are problems with elementary mathematics that tend to be simpler, more agile, and more clever. Here we are going to use elementary mathematics to solve some of the biggest and minor problems in physics. 1. Throw an object with the initial velocity v_0 vertically upwards, ask where is the highest point of this object and when? Let the distance between the highest point and the ground be h, and this object will reach its highest point in t seconds. Due to the gravitational pull of the Earth, objects thrown vertically upwards make a slow motion. Obviously the speed of the object at the highest point is equal to zero. and so