Please do part a and b And explain

A function can be represented as a Taylor Series i") (a) x) = E f n, (xa)" (10) 11:0 ' which is a power series in which the coefficients depend on the values of successive derivatives evaluated at a selected point. The notation here, which is commonly used is filial) = g ; WU?) = dZf (11) 2 dx x=a and so on. The \"zeroth derivative" is just the function value and, in formulas like this, 0! E 1. Suppose we pick the point a = 0 as our selected point. (a, 2 pts) Show that a Taylor Series expansion to second order (meaning up to n = 2 in the above formula) will exactly reproduce a quadratic function of the form g(x) : c0 + C1): + ngz (12) (b, 2 pts) What are the values of c0, c1, 2 in terms of the function value and derivatives of g evaluated at the point a : D? _ r