作者victor7935 (victor)
看板trans_math
標題[微分] 習題...
時間Sun Nov 9 19:07:32 2008
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
1F：→ Qmmm:第1題敘述是對的~ 140.112.128.93 11/09 19:33
2F：→ victor7935:= = '我還以為是故意寫這樣的說!!140.123.221.147 11/09 19:45
3F：→ victor7935:那我修一下好了..140.123.221.147 11/09 19:47
※ 編輯: victor7935 來自: 140.123.221.147 (11/09 19:47)
4F：→ Qmmm:第2題 令f(t)=cost-1+(1/2)t^2+(1/24)t^4 140.112.128.93 11/09 19:50
5F：→ Qmmm:由1階導數判別 x=0時為絕對極小值 140.112.128.93 11/09 19:51
6F：→ Qmmm:sorry 令f(x)=cosx-1+(1/2)x^2+(1/24)x^4 140.112.128.93 11/09 19:51
7F：→ Qmmm:所以f(x) > 0 for x > 0 ...就證出來了 140.112.128.93 11/09 19:52
8F：→ Qmmm:第三題一樣是一階導數可以作出來 140.112.128.93 11/09 19:54
※ 編輯: victor7935 來自: 140.123.221.147 (11/09 20:11)
9F：→ zptdaniel:第一題..隨便抓一個分段定義函數舉反例 123.194.99.216 11/09 20:40
10F：→ zptdaniel:domf=[0,4] not [1,3] 123.194.99.216 11/09 20:41
11F：→ zptdaniel:increasing not strictly increasing 123.194.99.216 11/09 20:41