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).
Famous quotes containing the word function:
“It is the function of vice to keep virtue within reasonable bounds.”
—Samuel Butler (18351902)