上海高考补习班上海高考辅导班新王牌.ppt

?第十二节(一)导数的应用上海新王牌教育 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?[主干知识梳理] ?一、函数的单调性?在(a,b) 内可导函数 f(x),f′(x)在(a,b)任意子区间内都不恒等于 0. ?f′(x)≥0?f(x)在(a,b)上为. ?f′(x)≤0?f(x)在(a,b)上为. 增函数减函数 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?二、函数的极值?: ?函数 y=f(x) 在点 x=a 的函数值 f(a) 比它在点 x=a 附近其它点的函数值都小, f′(a)=0 ,而且在点 x=a附近的左侧?,右侧,则点a 叫做函数 y=f(x) 的极小值点, f(a) 叫做函数y=f(x)的极小值. f′(x)<0 f′(x)>0 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?: ?函数 y=f(x) 在点 x=b 的函数值 f(b) 比它在点 x=b 附近的其他点的函数值都大, f′(b)=0, 而且在点 x=b附近的左侧?,右侧, 则点 b 叫做函数 y=f(x) 的极大值点, f(b) 叫做函数 y=f(x)的极大值. ?极小值点,极大值点统称为极值点,极大值和极小值统称为极值. f′(x)>0f′(x)<0 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?三、函数的最值?[a,b] 上连续的函数 f(x)在[a,b] 上必有最大值与最小值. ?2 .若函数 f(x)在[a,b] 上单调递增,则为函数的最小值, ?为函数的最大值;若函数 f(x)在[a,b] 上单调递减,则为函数的最大值, 为函数的最小值. f(a) f(b)f(a)f(b) Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?[基础自测自评] ?1.( 教材习题改编)若函数 f(x)=x 3+ ax 2+3x -9在x=- 3时取得极值,则 a等于() ? ?C. 4 ?D[∵f′(x)=3x 2+2 ax +3,f′(- 3)=0, ?∴a= 5.] Evaluation only. Evaluation only. Created with