where a is nonzero; or in other words, a polynomial of 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
If you set f(x) = 0, you get 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).
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