Question

A cube polynomial P is such that f(1)=1,f(2)=2,f(3)=3 and f(4)=5 then f(6) is​

Answer 1

Answer:

A cube polynomial P is such that f(1)=1,f(2)=2,f(3)=3 and f(4)=5 then f(6) is​

Step-by-step explanation:

Any polynomial of order n requires you to have n+1 data sets/information.

A linear polynomial/line y=ax+b requires two points to be defined completely.

A quadratic polynomial/parabola y=ax2+bx+c requires three points to be defined completely.

So, a 4th order polynomial will require 5 data sets.

If you consider f(x) in the above question as a 3rd order polynomial (assumption), then the question can be solved.

In general, one may assume f(x) as a 4th order polynomial and to solve it, assume the coefficient of highest order/leading coefficient as 1. There have been answers to this question in which people have solved it in rote ways. But, I would like to highlight the beauty of the problem by considering a 3 degree polynomial.