多元函數(shù)極值與一元函數(shù)極值的比較PPT學習教案

1、會計學1多元函數(shù)極值與一元函數(shù)極值的比較多元函數(shù)極值與一元函數(shù)極值的比較第1頁/共16頁)23,2, 0(sincos0sincos)0 , 0()sin,cos(3332 ff上的方向?qū)?shù)不存在。，函數(shù)在其它方向時的極限不存在時，即sincos0),(yxf，故在原點處0, 0), 0(, 0)0 ,(yxffyfxf第2頁/共16頁3ln3ln31xxx，而定義為函數(shù)3131| )(sgnxxx Plot3D Sign x* *yD D H HAbs x* *yD D L LH H13L L,8 8x,- -1, 1 ,8 8y,- -1, 1 , PlotPoints 30D D第3頁/

2、共16頁-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51第4頁/共16頁2222) 1() 1(),(xyxxyxff x_, y_D D:= = - -H Hx2- -1L L2- -H Hx2 y- -x- -1L L2第5頁/共16頁Solve 8 8D f x, yD D, xD D 0, D f x, yD D, yD D 0 ,8 8x, y D DPlot3D f x, yD D,8 8x,- -2, 2 ,8 8y,- -1, 4 ,PlotRange 8 8- -4, 0 , PlotPoints 30D D第6頁/共16頁Plot3D

3、 f x, yD D,8 8x,- -2, 2 ,8 8y,- -1, 4 , PlotRange 8 8- -4, 0 ,PlotPoints 30, ViewPoint 8 82.504,- -2.105, 0.867 D D-2-1012-101234-4-3-2-10-2-1012-2-1012-101234-4-3-2-10-4-3-2-10第7頁/共16頁第8頁/共16頁g x_, y_D D:= =3 x* *Ey- -x3- -EH H3 yL LSolve 8 8D g x, yD D, xD D 0, D g x, yD D, yD D 0 ,8 8x, y D D第9頁/

4、共16頁gy x_, y_D D:= =Evaluate D g x, yD D, yD D D D, 022xyyyxxxyyyxxgggggg和個，只要時），時）或極大值點（極小值點（的符號確定了該駐點為00,xxxxxxgggD g x, yD D,8 8x, 2 D D* *D g x, yD D,8 8y, 2 D D- -H HD g x, yD D, x, yD D L L2.8 8x 1, y 0 D g x, yD D,8 8x, 2 D D .8 8x 1, y 0 第10頁/共16頁, 6,272xxxyyyxxggggPlot3D g x, yD D,8 8x,- -3

5、, 3 ,8 8y,- -5, 3 , PlotRange 8 8- -100, 5 ,ViewPoint 8 81.571,- -2.901, 0.751 , PlotPoints 30D D第11頁/共16頁-202-4-202-100-75-50-250-202-4-202第12頁/共16頁-202-4-202-10-505-10-505Plot3D g x, yD D,8 8x,- -3, 3 ,8 8y,- -4, 2 , ViewPoint 8 82.631,- -1.943, 0.867 ,PlotRange 8 8- -10, 5 , PlotPoints 40, ClipFill NoneD D第13頁/共16頁-202-4-202-10-505-10-505Plot3D g x, yD D,8 8x,- -3, 3 ,8 8y,- -4, 2 , ViewPoint 8 82.985, 1.462, 0.6