.I'm really stuck on this problem...
If I let the function:
f : I→ I be continuous on I and differentiable on the open set I
for I := [0,1]
I know that theres at least 1 point t ∈ [0, 1] such that f(t) = t.
Now I need to use Rolle’s Theorem to show that if f'(x) is not equal to 1 in (0, 1), then there is exactly one such point t
This cannot be correct since is a counterexample...Perhaps it should be that in ? Because then it is easy to prove the point t must be unique...
I've tried 3 different proofs for this, but none of them are giving me uniqueness of t. Please help!