推 jacky7987 :好猛的Lagrange XDD 08/05 15:35
推 craig100 :高中新課綱有編拉個練舉 所以這題是必考題型 08/06 02:42
※ 引述《iddee ()》之銘言：
: 設 f(x) 是三次多項式且滿足
: f(1981) = 1
: f(1982) = 9
: f(1983) = 8
: f(1984) = 5
: 求 f(1985)
1*(x - 1982)*(x - 1983)*(x - 1984)
f(x) = -------------------------------------------
(1981 - 1982)*(1981 - 1983)*(1981 - 1984)
9*(x - 1981)*(x - 1983)*(x - 1984)
+ -------------------------------------------
(1982 - 1981)*(1982 - 1983)*(1982 - 1984)
8*(x - 1981)*(x - 1982)*(x - 1984)
+ -------------------------------------------
(1983 - 1981)*(1983 - 1982)*(1983 - 1984)
5*(x - 1981)*(x - 1982)*(x - 1983)
+ -------------------------------------------
(1984 - 1981)*(1984 - 1982)*(1984 - 1983)
f(1985) = 1 * (6)/(-6) + 9 * (8)/(2) + 8 * (12)/(-2) + 5 * (24)/(6)
= -1 + 36 - 48 + 20 = 7
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