Quartic function

A quartic function is a function of the form

:$f(x)=ax^4+bx^3+cx^2+dx+e\; ,$

with nonzero "a"; or in other words, a polynomial function with a degree of four. Such a function is sometimes called a biquadratic function, but the latter term can occasionally also refer to a quadratic function of a square, having the form

:$ax^4+bx^2+c,\; ,$

or a product of two quadratic factors, having the form

:$(ax^2+bx+c)(dy^2+ey+f).\; ,$ Since a quartic function is a polynomial of even degree, it has the same limit when the argument goes to positive or negative infinity. If "a" is positive, then the function increases to positive infinity at both sides; and thus the function has a global minimum. Likewise, if "a" is negative, it decreases to negative infinity and has a global maximum.

The derivative of a quartic function is a cubic function.

On finding the "roots", see Quartic equation.