Quartic Function

In mathematics, a quartic function, or equation of the fourth degree, is a function of the form

where a is nonzero; or in other words, a polynomial of degree 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

Setting results in a quartic equation of the form:

where a ≠ 0.

The derivative of a quartic function is a cubic function.

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 quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one where the coefficients can take any value).