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## Main Question or Discussion Point

Can someone help me with this?

Let f: R into R be differentiable

1) If there is an M strictly less than 1 for each x in R, f'(x) strictly less than M,

prove that there exists a unique point x such that f(x)=x. ( Note: x is a fixed point for f)

2) Give counter example to show 1) fails if M=1.

Let f: R into R be differentiable

1) If there is an M strictly less than 1 for each x in R, f'(x) strictly less than M,

prove that there exists a unique point x such that f(x)=x. ( Note: x is a fixed point for f)

2) Give counter example to show 1) fails if M=1.