Suppose f(t) can be written in a Taylor series representation centered at a number a as f"" (a) 6 -(t-a) + Suppose h> 0 below. a. Substitute t = x + h and a = x above and write the result. b. Substitute t = x - h and a = x above and write the result. Combine the information from parts a and b to show that f'(a) can be written in the form f" (a) = N(h) + Kh + Kh + ... where K, K4, etc. are independent of h, and give an explicit formula for N (h). d. Explain why N (h) is an 0(h) approximation of f'(a). Do you recognize N (h)? Use N (h) and N to create an 0 (h4) approximation N (h) of f'(a). C. 1 f(t) = f(a) + '(a)(t a) +=''(a)(t a) + = e.