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(Differentiation 25 pts.) You are given the function f(t) = 5 + 3t + 213. (a) (25 points) Expand the function about the point to = 1 using Taylor Series up to (and including) the 2nd order term (i.e., the 2nd derivative term). (b) (10 points) Compute the approximate first derivative of f (t) about t; = 1 using two- point Forward difference and Central difference methods, with a step size of At = 0.5. Calculate the relative error incurred by these two approximations, with respect to the exact derivative of f(t) at t; = 1. (c) (5 points) Assume that f(t) represents the distance traveled by a moving body as a function of time. The mass of this body is 1. Using a 2nd order accurate finite difference method and At = 0.5, compute the net force acting on this body at time t; = 1