求下列函数的极值 :[br][/br][tex=7.357x1.571]1P9Pk9AfGMFd/jm70qzgeDRTywXRGGUjAMyhzdvmpmpK0/k654lU61fhRfJsL9tT[/tex];
解 [tex=7.357x1.571]1P9Pk9AfGMFd/jm70qzgeDRTywXRGGUjAMyhzdvmpmpK0/k654lU61fhRfJsL9tT[/tex],[tex=11.786x1.571]iYCiXouHdyZSwmm7Tft3FoC62b/TY+FuotW9ZrP1J+BjrAQDlTTzHD0/dk9kfx5eOj9L3B9+a14/tyyj8ENH5Hm5kQ+q6zraOPABTvIJreA=[/tex][tex=6.571x1.286]6JLVVu8iP3mVCO1HsJaVXFUR02msa+2WmQ388rVQWto=[/tex][tex=11.929x6.357]luxnYXPz0zFuH3jflAxrJs2Jch80Dh7xaNhPq30zjHZGZitzX0ELCiqcnHy9SUZTJ50vDFoEQnv/GRD4FvB773kc4qC3v+vIriimVXo9DXM61odxWc63MdQ8F9HLLb2Vh12Im/K36qL+mB5bM5zZ7HYm36DAMPyEdjqU4cR+j84=[/tex]由[tex=3.5x1.429]77kBfjdnkpW2NUZ9x09UfA==[/tex], 得稳定点[tex=4.286x2.643]yo37Y9zlzyoPovXxML1bVBMq9GrXBZrzRvh/BccWtI0=[/tex],[tex=3.5x2.643]DOex94n1fRGk/XnHK6to1vDEdmgczEqDg+8maFc8x7o=[/tex], 且[tex=2.214x1.214]E5zEH+vMtzZBzVfcKvR2dg==[/tex], [tex=3.0x1.214]H0dNE6XP0hpq/J+fQggBsw==[/tex], [tex=2.214x1.214]hH31woL7JZD8RvMixcVpfA==[/tex] 处导数不存在.[br][/br]当[tex=7.143x2.643]f3o17yqkME6mzj5UZ22QBDOCvg8LFTELh6S2d3ibpqU=[/tex]时[tex=4.071x1.429]x4HteJ7Oj5SatZfauQgmqA==[/tex];当[tex=6.357x2.643]FUk1r5Li05ygBOBxwNZNZAZFS7IyImCW2AcKUTqkidM=[/tex]时[tex=4.071x1.429]P8txkwB7ouEK7WdoKHHpAA==[/tex] . 故[tex=8.286x3.357]7pdxTUqHbjXsbiu2G435gGUS05CUsErvxTozKuVyO/gPL1UwDy2pIV0WpMa7dFYXUgX8BS3qdOXB3vkt8zcTzg==[/tex]为极大值.[br][/br]当 [tex=5.429x2.643]NfdEpbUR3BGPkf2Dq2CR/uVJPObO+2ZttF6KDv8OLiQ=[/tex]时[tex=4.071x1.429]x4HteJ7Oj5SatZfauQgmqA==[/tex] ; 当[tex=5.429x2.643]9y6haaPFVFRA+LF0Bznr+cZJ3DDizdMElYsT8+38QkQ=[/tex]时[tex=4.071x1.429]P8txkwB7ouEK7WdoKHHpAA==[/tex] . 故 [tex=7.286x3.357]0/N2UwkjBi4H26ZIb5y5Wcm4GGvY/pvfDqPgpWjcN97RurZSjUSFWaL8lImLp6ur/GRq/VxFYeL8rN43W5S1Fg==[/tex]为极大值.[br][/br]由[tex=5.143x1.357]k3A0/vjeHkFfuMtVkDOrGA==[/tex][tex=3.857x1.357]kzSBQay5fKuRoiXV13m2pQ==[/tex], 且[tex=3.714x1.357]pRQ9HFEknmH8lHcZs8mqrMcABUFRvN2SGdTylE7at7g=[/tex]得[tex=5.143x1.357]k3A0/vjeHkFfuMtVkDOrGA==[/tex][tex=3.857x1.357]kzSBQay5fKuRoiXV13m2pQ==[/tex]为极小值. 故当[tex=4.214x2.643]kLCguSX7TQIAxEFYiRxdWMfbvp8cxy1XOToxZ1JTQ6Y=[/tex]时[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]取极大值[tex=2.357x2.357]NRY4QPYPiHs8r97Y+GDnRBhuNx82u57opNhC6CSA5KU=[/tex]; 当[tex=3.857x1.214]VX/eQAknS5u1NKlbq6Yb0w==[/tex]时[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]取极小值[tex=0.5x1.0]Sc0he7miKB3YF9rgXf2dDw==[/tex].
举一反三
- 求函数[tex=9.571x1.571]apbD0nRmlcdVZi5bj1fGfFnEk1XQpWZJehT+sYItVd4Fk+oX14reG5d1J4e3R4/9[/tex][tex=5.786x2.5]YHwiPugA06KcPVx+cUYIeakNgu/KTr77Yx6QhGSIqgg3vawn9kNKnqpPK/mfQ4AQ[/tex]的极值。
- 求下列函数的极值[br][/br][tex=5.857x1.5]8YiQ/jeNbzTYsp9RAU5SRQAnxqFbjca2tUHim5bXQac=[/tex]
- 下列程序的输出结果是( )。[br][/br] x=0[br][/br] k=10[br][/br] while k>0:[br][/br] k-=1[br][/br] if k[5:<br] break[br][/br] x+=1[br][/br] print(x) A: 5 B: 7 C: 9 D: 10
- 设函数 [tex=12.571x2.357]OHpHlp08spOzUuoW7DEI8UQGU5oI0ymbpfLTaAsQGVreaSPi+43aPyPx6TTq0MR0BO0kwCd0ZA/DFao4/+UdUA==[/tex][br][/br]求[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]的极值,并证明函数[tex=2.786x1.357]g1Wo3ALRzTk0js5m9GO2sA==[/tex]在点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 处不取极值.[br][/br][br][/br]
- 设随机变量(X,Y)的联合密度函数为p(x,y)=k(6-x-y),0求(1)系数k ;[br][/br] (2)P(X<1,Y<3)。
内容
- 0
求下列函数的导函数:(1) [tex=5.143x1.571]KFVqO28u784vV0YQYHthI0KsTnLorypr2wsRUIJCU0Q=[/tex][br][/br](2)[tex=5.0x1.714]t5tBVF4e6MbnN+Z3tG1H4RTO3b+ducOa9Wk0ONWtlxY=[/tex]
- 1
求下列函数的偏导数:[tex=5.5x1.571]p/AlKCi3aSRwX1SMwtz/1OFvxlx1ZOZCQlhcOu472PQ=[/tex][br][/br]
- 2
同时掷2颗均匀骰子,X表示点数大于4出现的个数,则以下结果正确的是 A: X服从二项分布 B: P(X=0)=P(X=1) C: P(X=1)=4/9 D: P(X=0)=1/9 E: P(X=2)=4/9 F: P(X>;0)=1 G: P(X<;2)=5/9 H: P(X>;1)>;0.5
- 3
求下列函数 [tex=1.643x1.357]Wfem9oxh0ZS7nZ3KGomKoQ==[/tex] 的像函数 [tex=1.929x1.357]CsHYmgN8a4Yt6bxTnBWLzw==[/tex].[p=align:center] [tex=7.357x1.5]V92zCeihgNFbCDChhSEi98E8M59qocW5X5D7ZDTewTInQoHiPouyg2FdZodvC/Eh[/tex][br][/br]
- 4
求下列函数的全微分:[tex=7.357x1.571]zU4xeCD33Ro5+mWZ3rGeLXVFF6pw0hNQcujVJ6GoR0FgsoG0QXV6EA52JeklwTod[/tex]