Question: Suppose that f : [a, b] [c, d] is differentiable and onto. If f' is never zero on [a, b] and d - c

Suppose that f : [a, b] → [c, d] is differentiable and onto. If f' is never zero on [a, b] and d - c > 2, prove that for every x ∈ [c, d] there exist x1 ∈ [a, b] and x2 ∈ [c, d] such that |fʹ(x1)(f-1,(x) - f-1(x2))| = 1.

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