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Second Derivatives and Applications
Definition of the second derivative, concavity, inflexion points
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Exercises
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Definition of the second derivative, concavity, inflexion points
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
No exercises available for this concept.
The derivative of the derivative of a function is its second derivative:
We determine concavity by the sign of f′′:
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At a stationary point (f′(a)=0),
If f′′(a)>0, then f has a local minimum at x=a.
If f′′(a)<0, then f has a local maximum at x=a.
Using the second derivative to classify a stationary point is often called the second derivative test.
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Inflexion points occur when f′′(x)=0 and f′′(x) changes sign. 🚫
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