Quartic function

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Image:Polynomialdeg4.png A quartic function is a function of the form

<math>f(x)=ax^4+bx^3+cx^2+dx+e</math>

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

<math>ax^4+bx^2+c</math>,

or a product of two quadratic factors, having the form

<math>(ax^2+bx+c)(dy^2+ey+f)</math>.

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.