Extremum Test
Consider a function 
in 1-D. If has a relative extremum at 
, then either 
or 
isnot Differentiable at . Either the first or second Derivative tests may be used to locate relativeextrema of the first kind.
A Necessary condition for to have a Minimum (Maximum) at is
and
A Sufficient condition is
and 
(
). Let , 
, ...,
, but 
. Then has a Relative Maximum at if 
is Odd and
, and has a Relative Minimum at if is Odd and 
. There is aSaddle Point at if is Even.See also Extremum, First Derivative Test, Relative Maximum, Relative Minimum,Saddle Point (Function), Second Derivative Test- Stella Octangula
- Stella Octangula Number
- Stellated Polyhedron
- Stellated Tetrahedron
- Stellated Truncated Hexahedron
- Stellation
- Stem-and-Leaf Diagram
- Step
- Step Function
- Step Polynomial
- Steradian
- Stereogram
- Stereographic Projection
- Stereology
- Stern-Brocot Tree
- Stevedore's Knot
- Stewart's Theorem
- Stickelberger Relation
- Stick Number
- Stiefel Manifold
- Stiefel-Whitney Class
- Stiefel-Whitney Number
- Stieltjes Constants
- Stieltjes Integral
- Stieltjes' Theorem