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The other Markov's inequality
f a polynomial function is trapped in a box, how much can it wiggle? This question is answered by Markov’s inequality, which states that for a degree- polynomial that maps into , it holds that (1)That is, if a polynomial is trapped within a square box , the fastest it can wiggle—as measured by its first derivative—is the square of its degree. How tight is this inequality? Do polynomials we know and love come close to saturating it, or is this bound very loose for them? A first polynomial which is natural to investigate is the power .
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