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# If a real root of a polynomial has an odd multiplicity of 3, 5, 7, 9 (any odd number bigger than 1), ...?

is it always the case that the graph has an inflection point at such root?

### 1 Answer

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- ted sLv 71 month ago
YES,,,,,f(x) = ( x - a)^(2n+1) ====> f ' ' (x) = C(x-a)^(2n-1)=====> sign change at the root ===> concavity changes

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