Differentiation and Stationary Points | 微分与驻点

📚 Differentiation and Stationary Points | 微分与驻点

In AQA A-Level Mathematics, questions on stationary points often appear in the classic (a), (b), (c) format: (a) differentiate a given function, (b) find the coordinates of the stationary points, and (c) determine the nature of each stationary point. This article breaks down this exact structure step by step, with the worked examples and exam language you need to secure full marks.

在 AQA A-Level 数学考试中，驻点相关问题常以经典的 (a)、(b)、(c) 三段式出现：(a) 对给定函数求导，(b) 求出所有驻点的坐标，(c) 判断每个驻点的性质。本文逐步骤拆解这一结构，配合完整例题与考试常用表达，帮助你稳稳拿到满分。

1. The Power Rule and Basic Differentiation | 幂法则与基本微分

Every (a) part in an AQA stationary-point question begins with differentiation. The single most important rule is the power rule: if y = xⁿ, then dy/dx = n xⁿ⁻¹. You must also remember that constants differentiate to zero, and that a constant multiple stays in front of the term.

每一道 AQA 驻点题目的 (a) 部分都从求导开始。最重要的法则是幂法则：若 y = xⁿ，则 dy/dx = n xⁿ⁻¹。同时必须记住：常数求导为零，常数倍数保留在对应项的前面。

For example, to differentiate f(x) = x³ – 6x² + 9x + 2, we bring each power down as a multiplier and reduce the exponent by one:

例如，对 f(x) = x³ – 6x² + 9x + 2 求导时，我们把每个幂

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