The number of passengers on a certain bus to Houston at any given time is given by the equation $P=−2(S−4)2+32$, where $P$ is the number of passengers and $S$ is the number of stops that the bus has made since the beginning of its route

题目

The number of passengers on a certain bus to Houston at any given time is given by the equation $P=−2(S−4)²+32$, where $P$ is the number of passengers and $S$ is the number of stops that the bus has made since the beginning of its route. If the bus begins its route without any passenger, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

选项

解析

仔细观察你会发现，当S=4时，P取得最大值32。因为无论你为S选择什么数值，都会从32中减去一个数，只有当S=4时，减去的部分为0，此时P=0+32=32。题目要求我们找到P取得最大值之后第2个站点的P值，因此需要计算S=4+2时的P值： \[ P = -2(6-4)^2 + 32 = 24 \] 选项C正确。还有一个解决这类题的快捷方法：如果你遇到需要求一个式子的最大值或最小值的问题，可以对其求导，步骤如下： \[ \frac{dP}{dS} = -2 \times 2(S-4)(-1) \] 令导数等于0（这是利用求导求函数最大值/最小值的方法，操作很简单，你可以在YouTube上搜索相关内容学习），可以解得S=4，这说明当S=4时，P取得最大值。

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