Recall that x is called a ﬁxed point of a function f(x) if f(x) = x.
Let f : [0, 1] ! [0, 1] be a continuous function and suppose also that f is
differentiable on (0, 1). Assume that f
0
(x)

Question

Recall that x is called a ﬁxed point of a function f(x) if f(x) = x.
Let f : [0, 1] ! [0, 1] be a continuous function and suppose also that f is
differentiable on (0, 1). Assume that f
0
(x) < 1 for all x 2 (0, 1). Prove that f
has precisely one ﬁxed point.

zzr0ck3r · Answer

sorry the notation is killing me
what is !
what is 
Assume that f
0
(x) < 1 for all x 2 (0,1)

anonymous · Answer

Sorry should be this question.
Two runners start and end the race at the same time. Prove that at
some time during the race they have the same speed.