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Mathematics-Online course: Prepcourse Mathematics - Analysis - Extrema and Curve Sketching

Inflection Points

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At an inflection point $ a$ of a function $ f$ the second derivative changes the sign.
\includegraphics[width=8.4cm]{Wendepunkt.eps}
Necessary is that $ f''(a)=0$ ; sufficient is that $ f'''(a)\ne0$ .

The figure shows a cubic polynomial.
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As the second derivative is linear, there exists exactly one inflection point.
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  automatically generated 10/23/2009