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# Quartic function

A quartic function is a function of the form

$f\left(x\right)=ax^4+bx^3+cx^2+dx+e ,$

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

$ax^4+bx^2+c, ,$

or a product of two quadratic factors, having the form

$\left(ax^2+bx+c\right)\left(dy^2+ey+f\right). ,$
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.

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