Understand the concepts of concavity and points of inflection and their relationship with the second derivative.

mm-u3-t3-s1-d3

Interactive

Concavity and points of inflection

manipulative

Scrub x on a curve with its concavity shaded; the tangent sits below where f″ > 0, above where f″ < 0, and swaps side exactly at an inflection.

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