![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polynomialdeg3.svg/640px-Polynomialdeg3.svg.png&w=640&q=50)
Cubic function
Polynomial function of degree 3 / From Wikipedia, the free encyclopedia
In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to complex numbers. In other cases, the coefficients may be complex numbers, and the function is a complex function that has the set of the complex numbers as its codomain, even when the domain is restricted to the real numbers.
This article relies largely or entirely on a single source. (September 2019) |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polynomialdeg3.svg/320px-Polynomialdeg3.svg.png)
Setting f(x) = 0 produces a cubic equation of the form
whose solutions are called roots of the function. The derivative of a cubic function is a quadratic function.
A cubic function with real coefficients has either one or three real roots (which may not be distinct);[1] all odd-degree polynomials with real coefficients have at least one real root.
The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point. Up to an affine transformation, there are only three possible graphs for cubic functions.
Cubic functions are fundamental for cubic interpolation.