[微分] 101 東華計算(3)

看板trans_math作者EggAche (蛋疼)時間9年前 (2015/06/11 16:39)推噓0(0推 0噓 4→)

留言4則, 2人參與討論串1/2 (看更多)

A real number c such that f(c)=c is call a fixed point of the function f. Prove that if f is differentiable and f'(x)≠1 for all x in an interval I, then f has at most one fixed point in I. 之前在書上遇到的都是給定 x=0 x=1 的條件配合具備連續性而有的中間值定理來證明, 今天條件只給了可微分(暗中應該也是給了連續的條件), 又 f'(x)≠1 就沒什麼頭緒了... 這類存在性定理的證明感覺會和均值定理有關係，能給些思路嗎? -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.120.50.155 ※ 文章網址: https://www.ptt.cc/bbs/trans_math/M.1434011946.A.F3C.html

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keith291

06/11 16:57, , 1^F

06/11 16:57, 1^F

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EggAche

06/11 17:00, , 2^F

06/11 17:00, 2^F

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keith291

06/11 17:00, , 3^F

06/11 17:00, 3^F