作者caxz (虚幻梦影)
看板trans_math
标题[微分] 微分的证明题
时间Wed Jun 20 15:51:41 2007
(1)
f(x),f'(x) and f''(x) are all continous on I
Suppose x=a is a critical point of f(x)
show that
(i)If f''(x)≧0 for all x属於I
then x=a is a global minimizer of f(x)
(ii) If f''(x)>0
then x=a is a strict local minimizer of f(x)
(提示 用泰勒展开证明之)
(2)
Show that any continous function f:[0,1]->[0,1] has at least one fixed point
(i.e. 存在c属於(0,1)-> f(c)=c )
(3)
{ 1 , x>0 y>0
f(x,y) = { 0 , o.w.
show that f_x and f_y both existat(0,0) but it is not differentiable at (0,0)
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1F：→ siriusinlove:第1题应该不用到泰勒吧第2用I.v.t 61.228.181.195 06/21 02:00
2F：→ siriusinlove:第3用偏微跟可微的极限的定义 61.228.181.195 06/21 02:01