Finding the cubic equation

Question

Find the cubic equation:

for which

f(-1)=3

f(1)=1

f(2)=6

and f(3)=7.

Answer 1

This is an exercise in arithmetic.

Substitution will give you 4 linear equations in unknowns a, b, c, & d.

You can use Gaussian elimination to solve that system...or more rationally you can plug the coefficients into a spreadsheet and invert the matrix! Good luck.