[高二数学选修2-2~2瞬时变化率.ppt

* 1.1.2导数的概念 ——瞬时变化率1 苏教高中数学选修2-2 * Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 研究对象 变化 数学模型 不足之处 变化的快慢 平均变化率 需要严格的数学定义! 对变化过程的反映不够精细! y2－y1 不能反映变化的过程! 问题情境 数量化 视觉化 有待于进一步精确化，随之而来的便是新的数学模型的建立. 回顾反思:平均变化率 平均变化率的作用? 利用其可近似地刻画了曲线在某一区间上的变化趋势. 无数不入微 无形不直观 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 回顾反思:平均变化率 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1.如何精确地刻画曲线在一点处的变化趋势? 放大 p p p 再放大 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. p p 放大 再放大 p p p p 再放大 放大 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 结论2：点P附近的曲线被看作直线, 从而,该直线的斜率便量化了曲线经 过点P时上升或下降的“变化趋势”. 结论1：在点p附近,曲线可以看作直线 （即在很小的范围内以直代曲）. p Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2. 如何找到在曲线上一点p处最逼近曲线的直线L呢? L1 L2 x o y p (1)试判断哪一条直线在点p附近 更加逼近曲线. (2) 在点p附近你能做出一条比 L1,L2更加逼近曲线的直线L3吗? Q p为曲线上一点,Q为曲线上另一点. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. P Q o x y y=f(x) 割线 切线 T 2. 如何找到在曲线上一点p处最逼近曲线的直线L呢? Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1.直线PQ称为曲线的割线. 2.在点p处最逼近曲线的直线称为曲线在点p处的切线. 3.如何计算在曲线上一点p处切线L的斜率呢? Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 如图,设曲线C上一点 x o y p Q 割线 过点p的一条割线交曲线于一点 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. x o y p Q 割线 则割线PQ的斜率为: Evaluation only. Created with Aspos