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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.
Patterns of Inflection
Age 16 to 18
Challenge Level 
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.
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