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Applications of differentiation

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Stationary and non-stationary inflections

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Graphs of x³, x³+x and x⁴. Both cubics change concavity at 0: the first has zero slope there, the second slope 1. The quartic has second derivative zero at 0 but no change of concavity.
Graphs of x³, x³+x and x⁴. Both cubics change concavity at 0: the first has zero slope there, the second slope 1. The quartic has second derivative zero at 0 but no change of concavity.
Graphs of x³, x³+x and x⁴. Both cubics change concavity at 0: the first has zero slope there, the second slope 1. The quartic has second derivative zero at 0 but no change of concavity.
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