[微分] 習題...

[victor7935 (victor)]

1.
  If f'(X)=0 at x=1,x=2,x=3,then f cannot possibly increase on[0,4].

     這是對的!!...簡單證明
2.
  Show that cosx < 1 - (1/2)x^2 + (1/24)x^4  for all x >0.

3.
  Show that the equation P(x)=0 has exactly two real roots,

  both positive.

 P(x)= x^4 - 8x^3 + 22x^2 - 24x + 4

4.Prove that a polynomial of degree n has at most n-1 local extreme values.


5.Let f be differentiable on an open interval I.Prove that,if f'(x) = 0

    for all x in I,then f is constant on I.

感覺.....

 這些問題感覺對大家來說都很簡單!?

     有時候都不知道該不該問了= = ....

  自己好像還想得不夠多....


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◆ From: 140.123.221.147
→ Qmmm:第1題敘述是對的~
→ victor7935:= = '我還以為是故意寫這樣的說!!
→ victor7935:那我修一下好了..
※ 編輯: victor7935      來自: 140.123.221.147      (11/09 19:47)
→ Qmmm:第2題 令f(t)=cost-1+(1/2)t^2+(1/24)t^4
→ Qmmm:由1階導數判別 x=0時為絕對極小值
→ Qmmm:sorry 令f(x)=cosx-1+(1/2)x^2+(1/24)x^4
→ Qmmm:所以f(x) > 0  for x > 0  ...就證出來了
→ Qmmm:第三題一樣是一階導數可以作出來
※ 編輯: victor7935      來自: 140.123.221.147      (11/09 20:11)
→ zptdaniel:第一題..隨便抓一個分段定義函數舉反例
→ zptdaniel:domf=[0,4] not [1,3]
→ zptdaniel:increasing not strictly increasing
→ muxiv       : 第2題 令f(t)=c http://yofuk.com