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f(x) ≥ 0 for all x ∈ (0, 1) and its third derivative f ^3(3)(x) exists...

f(x) ≥ 0 for all x ∈ (0, 1) and its third derivative f ^3(3)(x) exists for all x ∈ (0, 1). If f(x) = 0 for two different values of x in (0, 1), prove that there exists a c in (0, 1) such that f ^(3)(c) = 0.

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