First, I would like to thank any help provided, I truly appreciated.
Here's my problem:
Consider the function 𝑓(𝑥)=3𝑥^3+𝑥.
a. Without MATLAB, compute the first 5 (𝑛 = 0,1,2,3,4) Taylor Series coefficients (Cn) for the function about 𝑎=2.
After computation I got:
3x^3+x approx 26 + 37(x-2) + 18(x-2)^2 + 3(x-2)^3 + 0(x-2)^4
So, the first thing I noticed was that the fuction is not infinitely differentiable since the fourth derivative is zero and so on.
b. How many terms in the Taylor Series would you need for a good approximation of this target function? Justify your answer in three sentences or less.
HERE is where I'm having trouble and is simply because I might be missing something about Taylor Series, but I understand that having 5 and 4 terms would be exacly the same since the last of the 5 term is zero, regardless, I have tried 3 terms, got the relative error, and it is soo similar to having 4 terms. The difference is so big between the function and the taylor polynomial when x=0 or any other number, that is not even an approximation...
Thanks for the help!