Quartic Function

A quartic function is a function of the form f of x equal to a x to the fourth plus b x cubed plus c x squared plus d x plus e, with a nonzero, defined by a polynomial of degree four called a quartic polynomial, and a quartic equation sets such a polynomial equal to zero. Its derivative is always a cubic function, and because the polynomial has even degree the function tends to the same infinite limit in both directions, giving it a global minimum when a is positive and a global maximum when a is negative, with the possibility of one further local maximum and minimum in between. Degree four is the highest degree for which every polynomial equation can be solved by radicals, a limit fixed by the Abel-Ruffini theorem.