函数的最大[最小]值.ppt

1阅读P30，什么函数的最大值？最小值？ 2 阅读例3例4，怎样求二次函数的最大值？ 3 阅读例4，怎样求单调函数的最大值？ 1做优化P30例2 2 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 函数的最大（小）值 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1. 什么是单调函数?怎样证明？ 2. 什么是函数最大值? 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. 新知初探思维启动 最大值和最小值 条件 结论 几何意义 最大值 一般地，设函数y＝f(x)的定义域为I，如果存在实数M满足：对于_____的x∈I，都有 f(x)______ M 存在x0∈I，使得___________ 称M是函数y＝f(x)的最大值 f(x)图象上最______点的纵坐标 最小值 f(x)______ M 称M是函数y＝f(x)的最小值 f(x)图象上最______点的纵坐标 任意 ≤ ≥ f(x0)＝M 高 低 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 想一想 所有的单调函数都有最值吗？ 提示：不一定，如y＝2x＋1没有最值． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 做一做 1.函数y＝2x－3在区间[－1,2]上的最小值与最大值分别为(　　) A．－2，－1　　　　　　　　　 B．－5,1 C．－1,2 D．－4,1 答案：B Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2．函数y＝－x2＋2x的最大值是________． 答案：1 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. 典题例证技法归纳 题型一　利用图象求函数最值 已知函数f(x)＝|x＋1|＋|x－1|. (1)画出f(x)的图象； (2)根据图象写出f(x)的最小值． 题型探究 例1 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. 【名师点评】　图象法求函数y＝f(x)最值的步骤： (1)画出函数y＝f(x)的图象； (2)依据函数最值的几何意义，借助图象写出最值． Evaluation only. Created with Aspose.Slides fo