Cubic Function

Cubic function is a polynomial function of degree 3

AKA: Third-Order Polynomial.
Context:
- It can be a Univariate or a Multivariate function.
Example(s):
- [math]\displaystyle{ ax^3+bx^2+cx+d, \quad a \ne 0 }[/math].
- [math]\displaystyle{ f(x,y) = a x^3 + by^3 + cx^2+dx^2+ex y+ f x+ gy + h, \quad a \ne 0, \quad b \ne 0 }[/math].
- …
Counter-Example(s):
- a Linear Function.
- a Quadratic Function.
See: Cubic Equation, Polynomial Function, Complex Number, Algebra, Function (Mathematics), Root of a Function, Polynomial, Coefficients, Real Number, Degree of a Polynomial, Algebraic Function, Quadratic Function, Quartic Function, Abel–Ruffini Theorem.

References

(Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Cubic_function Retrieved:2017-6-11.
- In algebra, a cubic function is a function of the form : [math]\displaystyle{ f(x)=ax^3+bx^2+cx+d }[/math] in which is nonzero.
  Setting $f (x) 0$ produces a cubic equation of the form : [math]\displaystyle{ ax^3+bx^2+cx+d=0.\, }[/math] The solutions of this equation are called roots of the polynomial $f (x)$ . If all of the coefficients , , , and of the cubic equation are real numbers then there will be at least one real root (this is true for all odd degree polynomials). All of the roots of the cubic equation can be found algebraically. (This is also true of a quadratic or quartic (fourth degree) equation, but no higher-degree equation, by the Abel–Ruffini theorem). The roots can also be found trigonometrically. Alternatively, numerical approximations of the roots can be found using root-finding algorithms like Newton's method.
  The coefficients do not need to be complex numbers. Much of what is covered below is valid for coefficients of any field with characteristic $0$ or greater than $3$ . The solutions of the cubic equation do not necessarily belong to the same field as the coefficients. For example, some cubic equations with rational coefficients have roots that are non-rational (and even non-real) complex numbers.