A quartic function is a function of the form
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
or a product of two quadratic factors, having the form
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.