Given the data for an experiment:
Velocity: 0, 2, 4, 6, 8, 10
Force: 0 , 2.9, 14.8, 39.6, 74.3, 119
(One force value listed below one velocity value in a table)
Find an interpolating polynomial $p(t) = a_0 + a_1 t + a_2 t^2 + a_3 t^3 + a_4 t^4 + a_5 t^5$ for these data.
What happens if you try to use a polynomial of degree less than 5?
(This is a MATLAB question, but our class was never taught how to answer this kind of question in the first place)