Module 13 :  Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 38 :  Second derivative test for local maxima / minima & saddle points [Section 38.1]
 

Thus,

Further,

and

Thus,

   
38.1.5 Remark:
 

The Discriminant test is inconclusive at when



For details see next examples.

   
38.1.6 Examples:
(i)
The function
 


has a local maximum at even though

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