拉格朗日插值多项式可以解决你的问题!
我给你写哈
f(6)=505
f(7)=1425
f(11)=5104
f(25)=23975
f(33)=33786
f(40)=42371
f(x)
=42371*[(x-6)(x-7)(x-11)(x-25)(x-33)/(40-6)(40-7)(40-11)(40-25)(40-33)]
+33786*[(x-6)(x-7)(x-11)(x-25)(x-40)/(33-6)(33-7)(33-11)(33-25)(33-40)]
+23975*[(x-6)(x-7)(x-11)(x-33)(x-40)/(25-6)(25-7)(25-11)(25-33)(25-40)]
+5104*[(x-6)(x-7)(x-25)(x-33)(x-40)/(11-6)(11-7)(11-25)(11-33)(11-40)]
+1425*[(x-6)(x-11)(x-25)(x-33)(x-40)/(7-6)(7-11)(7-25)(7-33)(7-40)]
+505 *[(x-7)(x-11)(x-25)(x-33)(x-40)/(6-7)(6-11)(6-25)(6-33)(6-40)]