In mathematics, a quintic function is a function of the form
where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero. In other words, a quintic function is defined by a polynomial of degree five.
Setting g(x) = 0 and assuming a ≠ 0 produces a quintic equation of the form:
If a is zero but one of the other coefficients is non-zero, the equation is classified as either a quartic equation, cubic equation, quadratic equation or linear equation.
Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess an additional local maximum and local minimum each. The derivative of a quintic function is a quartic function.
Read more about Quintic Function: Finding Roots of A Quintic Equation, Beyond Radicals
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—Margaret Fairless Barber (1869–1901)