Convex Function
A function whose value at the Midpoint of every Interval in its Domain does not exceed theAverage of its values at the ends of the Interval. In other words, a function 
is convex on anInterval 
if for any two points 
and 
in ,
If
has a second Derivative in , then a Necessary and Sufficient conditionfor it to be convex on that Interval is that the second Derivative 
for all 
in .See also Concave Function, Logarithmically Convex Function
References
Eggleton, R. B. and Guy, R. K. ``Catalan Strikes Again! How Likely is a Function to be Convex?'' Math. Mag. 61, 211-219, 1988. Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1100, 1980.
- Quadratic Invariant
- Quadratic Irrational Number
- Quadratic Map
- Quadratic Mean
- Quadratic Reciprocity Law
- Quadratic Reciprocity Relations
- Quadratic Reciprocity Theorem
- Quadratic Recurrence
- Quadratic Residue
- Quadratic Sieve Factorization Method
- Quadratic Surd
- Quadratic Surface
- Quadratrix of Hippias
- Quadrature
- Quadrature Formulas
- Quadric
- Quadricorn
- Quadrifolium
- Quadrilateral
- Quadrillion
- Quadriplanar Coordinates
- Quadruple
- Quadruple Point
- Quadruplet
- Quadtree