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- Knot Sum
- Knot Theory
- Knot Vector
- Knödel Numbers
- Kochansky's Approximation
- Koch Antisnowflake
- Koch Island
- Koch Snowflake
- Koebe Function
- Koebe's Constant
- Kollros' Theorem
- Kolmogorov-Arnold-Moser Theorem
- Kolmogorov Complexity
- Kolmogorov Constant
- Kolmogorov Entropy
- Kolmogorov-Sinai Entropy
- Kolmogorov-Smirnov Test
- Korselt's Criterion
- Kovalevskaya Exponent
- Kozyrev-Grinberg Theory
- k-Partite Graph
- Kramers Rate
- Krawtchouk Polynomial
- Kreisel Conjecture
- Kronecker Decomposition Theorem