Problem 3: (20 points) In this problem, you will derive an expression for the centered finite divided difference approximation of the second derivative: "(x)= {(x,)2f(x) + f(x,_1) h 1) Write the 4th-order Taylor series expansions for f(x) and f(x-1) and manipulate them to obtain the above approximate expression for f'(x;) (Hint: I showed you a similar calculation in class when I derived the centered difference approximation for the first derivative). 2) What is the order of the error for this approximation? Justify your answer by using the results of the calculation that you performed in part 1. Broblem3 16th ander Tayler series expansions for frames) and frans) = + fax) = f(x) + (flash) + f (z) h ( forms) + (n-1) = 28(21) + 28" (30 h. of "h"-014) Is the Vocal