Question: 7. (10 points) Suppose f is a differentiable function with |f'($)| 7. (10 points) Suppose f is a differentiable function with < 1 for all

7. (10 points) Suppose f is a differentiable function with |f'($)|

7. (10 points) Suppose f is a differentiable function with < 1 for all e (a, b) and that a f (x) b for all a: G [a, b]. Use the mean value theorem to prove that f has a unique fixed point in (a, b) such that f (c) c.

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