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Basically integral inequality

Source: Moldova MO 2007 12th grade day I problem 4

March 3, 2007
calculusintegrationinequalitiesfunctioncalculus computations

Problem Statement

If the function f ⁣:[1,2]→Rf\colon [1,2]\to R is such that ∫12f(x)dx=7324\int_{1}^{2}f(x) dx=\frac{73}{24}, then show that there exists a x0∈(1;2)x_{0}\in (1;2) such that x02<f(x0)<x03x_{0}^{2}<f(x_{0})<x_{0}^{3} [Edit: ff is continuous]
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