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.
之前在书上遇到的都是给定 x=0 x=1 的条件
配合具备连续性而有的中间值定理来证明,
今天条件只给了可微分(暗中应该也是给了连续的条件),
又 f'(x)≠1 就没什么头绪了...
这类存在性定理的证明感觉会和均值定理有关系，
能给些思路吗?