题目
A curve has equation , where and is a constant. The curve has a stationary point at the point , which has -coordinate 9.
Find the -coordinate of .
题目中文翻译
一条曲线的方程为 ,其中 , 为常数。曲线在点 处有驻点, 的 坐标为 9。
求 的 坐标。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。
解答
解法一
思路
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驻点处一阶导数为零。先用横坐标确定 ,再代回原方程。
答题过程
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The derivative is . At it is zero, so and . The height is then .