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Patterns of Inflection

Stage: 5 Challenge Level: Challenge Level:1

A point of inflection of a curve $y=f(x)$ is a point at which the second derivative $\frac{d^2y}{dx^2}$ changes sign.

Geometrically, you can think of a point of inflection as a point where the tangent to the curve crosses the curve.
 
Points of inflection need not also be stationary points (first derivative also zero), although they might be.