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In algebra, an octic equation〔James Cockle proposed the names "sexic", "septic", "octic", "nonic", and "decic" in 1851. ((''Mechanics Magazine'', Vol. LV, p. 171 ))〕 is an equation of the form : where ''a'' ≠ 0. An octic function is a function of the form : where ''a'' ≠ 0. In other words, it is a polynomial of degree eight. If ''a'' = 0, then it is a septic function (''b'' ≠ 0), sextic function (''b'' = 0, ''c ''≠ 0), etc. The equation may be obtained from the function by setting ''f''(''x'') = 0. The ''coefficients'' may be either integers, rational numbers, real numbers, complex numbers or, more generally, members of any field. Since an octic function is defined by a polynomial with an even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If the leading coefficient 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, the octic function decreases to negative infinity and has a global maximum. The derivative of an octic function is a septic function. ==See also== *Cubic function *Quartic function *Quintic function *Sextic equation *Septic function *Polynomials 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Octic equation」の詳細全文を読む スポンサード リンク
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