[微分] 求救求救...都是我的問題!??

看板trans_math作者 (victor)時間17年前 (2008/11/09 23:50), 編輯推噓6(6推 0噓 21→)
留言27則, 4人參與, 6年前最新討論串1/2 (看更多)
1. Show that x - (x^3)/6 < sinx for all x > 0 微1次後 f(x) = sinx -x + (1/6)x^3 f'(x)= cosx -1 + (1/2)x^2 然後..... 2. Suppose that f is continuous on [a,b] and f(a)=f(b). Show that f has at least one critical point in (a,b). 3. (a) Give an example of a nonconstant function that takes on both its absolute max and absolute min on every interval. (b) Give an example of a nonconstant function that has an iinfinite number of distinct local max and an infinite number of distinct local min. 4.Use 1 - (1/2)x^2 < cosx < 1- (1/2)x^2 + (1/24)x^4 for all x>0. to estimate cos 6度(the x above is in radians.) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.123.221.147
→
11/10 00:02, , 1F
1.x=0為C.P.,f(0)=0為 absolute minmum.
11/10 00:02, 1F
→
11/10 00:02, , 2F
f(0) < f(x) , for all x>0
11/10 00:02, 2F
推
11/10 00:03, , 3F
1. let cosx=-1 then f'(x)=(1/2)x^2
11/10 00:03, 3F
→
11/10 00:03, , 4F
>0 for all x
11/10 00:03, 4F
→
11/10 00:03, , 5F
so f(x)遞增
11/10 00:03, 5F
→
11/10 00:03, , 6F
2.少了f在(a,b)可微的條件
11/10 00:03, 6F
→
11/10 00:04, , 7F
2. by Thm , true
11/10 00:04, 7F
→
11/10 00:05, , 8F
critical point是什麼點?
11/10 00:05, 8F
推
11/10 00:12, , 9F
2.f在[a,b]連續且f(x)=f(b)
11/10 00:12, 9F
→
11/10 00:12, , 10F
則f至少有一個臨界點在(a,b)
11/10 00:12, 10F
→
11/10 00:13, , 11F
f不需要可微
11/10 00:13, 11F
→
11/10 00:13, , 12F
f(a)
11/10 00:13, 12F
→
11/10 00:17, , 13F
那這樣是要有哪個定義證?!!
11/10 00:17, 13F
→
11/10 00:19, , 14F
用
11/10 00:19, 14F
※ 編輯: victor7935 來自: 140.123.221.147 (11/10 00:20)
→
11/10 00:21, , 15F
2. 考慮f(x)=|x| ,f is cont. everywhere
11/10 00:21, 15F
→
11/10 00:22, , 16F
f(1)=f(-1) 但f在(-1,1)不可微
11/10 00:22, 16F
※ 編輯: victor7935 來自: 140.123.221.147 (11/10 00:22)
推
11/10 00:25, , 17F
2. set f(x)=1 ,x no critical point
11/10 00:25, 17F
→
11/10 00:27, , 18F
所以不可微那點就是critical point!!
11/10 00:27, 18F
→
11/10 00:27, , 19F
是降嗎?
11/10 00:27, 19F
→
11/10 00:29, , 20F
嗯嗯~~ 不存在點也是臨界點 抱歉忘了^^"
11/10 00:29, 20F
→
11/10 00:32, , 21F
那就是分2種討論!? 1.可微..by MVT
11/10 00:32, 21F
→
11/10 00:33, , 22F
因為f(a)=f(b) ..f'(c)=0 ..2不可微.
11/10 00:33, 22F
→
11/10 00:33, , 23F
之點及是臨界點...這樣寫ok?
11/10 00:33, 23F
推
11/10 00:46, , 24F
3.(a) let f(x)=sin(x)
11/10 00:46, 24F
推
11/10 00:51, , 25F
3.(b) let f(x)=sec(x);(-pi/2,pi/2)
11/10 00:51, 25F
推
11/10 00:53, , 26F
4. x=0.104719667帶入
11/10 00:53, 26F
→
04/22 18:01, 6年前 , 27F
因為f(a)=f(b) https://noxiv.com
04/22 18:01, 27F
‣ 更多 victor7935 的文章
文章代碼(AID): #195mRTvo (trans_math)
‣ 更多 victor7935 的文章
文章代碼(AID): #195mRTvo (trans_math)