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?