Definition of the second derivative, concavity, inflexion points
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Practice exam-style second derivatives and applications problems
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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