作者Eliphalet (冇提就等於唔存在啦)
站内trans_math
标题Re: [微分] Real Root(s)
时间Sat Sep 13 13:27:37 2008
※ 引述《Qmmm (Q蛆蛆)》之铭言：
: 4
: How many real root(s) does the equation x + 4x+ 1= 0 have ?
: (1) at least 1 ;
: (2) at least 2 ;
: (3) at least 3 ;
: (4) at least 4 ;
: 请问这题该怎麽算呢？谢谢
令 f(x) = x^4 + 4x + 1 , x 属於 R
f'(x) = 4x^3 + 4 = 4 * ( 1 + x^3 )
=> f'(x) > 0 , if x > -1
f'(x) < 0 , if x < -1
f(-2) = 9 > 0 , f(-1) = -2 < 0 , f(0) = 1 > 0
=> 有两实根 α,β , -2 < α < -1 , -1 < β < 0
有错请指教
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◆ From: 122.127.102.192
1F：推 stillboy:这种题目通常都要证存在性与唯一性 114.44.228.87 09/13 19:53
2F：→ stillboy:你只证出存在性,还差唯一性 114.44.228.87 09/13 19:53
3F：→ stillboy:唯一性要用roll's thm才证 114.44.228.87 09/13 19:54
4F：→ stillboy:可以参考我写的5158那篇 :) 114.44.228.87 09/13 19:54
5F：→ Qmmm:我觉得题目说至少的话只要用中间值即可 202.151.57.79 09/15 11:05
6F：→ Qmmm:除非说exactly 202.151.57.79 09/15 11:05