Quartic function

Polynomial of degree 4: f(x) = (x+4)(x+1)(x-1)(x-3)/14+0.5

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.