** This is a different question than Intuition explanation of taylor expansion? **
I understand some of the intuition behind a Taylor/Maclaurin expansion. More specifically, I understand that adding higher and higher degree polynomials will add more 'turning points' on a graph to better represent the curves of the function you wish to approximate.
I don't understand why
a.) you add the terms; shouldn't adding terms shift the graph left/right, up/down? In addition to the question of shifting the graph, I just don't understand why you would add more terms, rather than just change your first term accordingly.
I now understand the above, thanks to microarm15 and Nicholas Stull. I now just do not understand part b of this question
b.) the terms added are the successive derivatives of the function. What does adding successive derivatives mean/give you?
Any help on the matter is greatly appreciated. Thanks!