Re: [微分] Real Root(s)

[Eliphalet (冇提就等於唔存在啦)]

※ 引述《Qmmm (Q蛆蛆)》之銘言：
:                                          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 ;
: 請問這題該怎麼算呢？謝謝


 令 f(x) = x^4 + 4x + 1 , x 屬於 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


 =>  有兩實根 α,β , -2 < α < -1 , -1 < β < 0


  有錯請指教









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◆ From: 122.127.102.192
推 stillboy:這種題目通常都要證存在性與唯一性
→ stillboy:你只證出存在性,還差唯一性
→ stillboy:唯一性要用roll's thm才證
→ stillboy:可以參考我寫的5158那篇 :)
→ Qmmm:我覺得題目說至少的話只要用中間值即可
→ Qmmm:除非說exactly