Question: Suppose that f is C1 on an interval (a, b). If f'(x0) 0 for some x0 (a, b), prove that there exist intervals

Suppose that f is C1 on an interval (a, b). If f'(x0) ≠ 0 for some x0 ∈ (a, b), prove that there exist intervals I and J such that f is 1-1 from I onto J and f-1 is continuously differentiable on J.

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