On the Second Derivative Test for Constrained Local Extrema

1985 ◽  
Vol 92 (9) ◽  
pp. 631-643 ◽  
Author(s):  
D. Spring
Keyword(s):  
Second Derivative ◽  
Local Extrema ◽  
Derivative Test

A more conclusive and more inclusive second derivative test

2020 ◽  
Vol 104 (560) ◽  
pp. 247-254
Author(s):  
Ronald Skurnick ◽  
Christopher Roethel
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Local Minimum ◽  
Local Maximum ◽  
Number Line ◽  
Second Derivative ◽  
First Derivative ◽  
Line Test ◽  
First Derivative Test ◽  
Derivative Test

Given a differentiable function f with argument x, its critical points are those values of x, if any, in its domain for which either f′ (x) = 0 or f′ (x) is undefined. The first derivative test is a number line test that tells us, definitively, whether a given critical point, x = c, of f(x) is a local maximum, a local minimum, or neither. The second derivative test is not a number line test, but can also be applied to classify the critical points of f(x). Unfortunately, the second derivative test is, under certain conditions, inconclusive.

A Strong Second Derivative Test

1975 ◽  
Vol 82 (3) ◽  
pp. 287-289
Author(s):  
J. H. C. Creighton
Keyword(s):  
Second Derivative ◽  
Derivative Test

A Strong Second Derivative Test

1975 ◽  
Vol 82 (3) ◽  
pp. 287
Author(s):  
J. H. C. Creighton
Keyword(s):  
Second Derivative ◽  
Derivative Test
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