Quartic function

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Graph of a polynomial of degree 4, with 3 critical points.

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.