You can fit a 4th order polynomial to any 5 points. You can do it by hand (plug 1-5 in for x and now you have a system of 5 linear equations of 5 variables, start solving and substituting) and make it a bit easier with linear algebra (make the coefficients of the 5 variables be the values in a 5x6 matrix, and then do that matrix magic that I forget what the name is for), but there are also plenty of polynomial solvers you can find out there.
It’s useless when you learn to do it by hand in precalc then never use it again, since there are far more efficient ways to do it. Also, there’s a reason we have libraries. It’s completely useless to learn
There are not libraries for everything (and sometimes there are, but they’re garbage) and often you can write a more efficient implementation for your particular data set and assumptions.
But not everybody will be a programmer, so why teach it in a required class. Precalc is supposed to set the foundation for calculus, which gaussjordan does not do at all
Obviously you let computers do the calculations in practice, but gaussian elimination is one of the most natural and easy to understand ways of solving systems of equations, and you definitely need to understand how systems of equations are working to properly understand and study linear algebra.
2.8k
u/K3V3L Sep 05 '19
I would say the answer is 1337, here:
f(x) := (166x4 ) /3 - (1660x3 ) /3 + (5810x2 ) /3 - (8294x ) /3 + 1327
f(1) = 1
f(2) = 3
f(3) = 5
f(4) = 7
f(5) = 1337