/sci/ - Science & Math

[math]
\text{Let }f\text{ be a real function on the real line with continuous third derivative. Prove}
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\text{that there exists a point }a\text{ such that}
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\qquad \qquad \qquad \qquad \qquad f(a)\cdot f'(a) \cdot f''(a) \cdot f'''(a)\geq 0 .
[/math]