Consider the following approximation: f'(x) A f(x - 2h) + B f(x - h) + C f(x) + Df(x + h) + E f(x + 2h). Determine the values of the constants A, B, C, D, and E so that the approximation is as accurate as possible. What is the order of the error? Please note this is (at least somewhat) a "pencil and paper" exercise. Suppose your answer to part 1) above was that the order of the error was O(h^p). Recall that in class we generated Matlab pictures showing a line of slope p (approximately) when we plotted log h on the horizontal axis and log error on the vertical axis. Produce such a picture for this approximation and compute the slope. Consider the following approximation: f'(x) A f(x - 2h) + B f(x - h) + C f(x) + Df(x + h) + E f(x + 2h). Determine the values of the constants A, B, C, D, and E so that the approximation is as accurate as possible. What is the order of the error? Please note this is (at least somewhat) a "pencil and paper" exercise. Suppose your answer to part 1) above was that the order of the error was O(h^p). Recall that in class we generated Matlab pictures showing a line of slope p (approximately) when we plotted log h on the horizontal axis and log error on the vertical axis. Produce such a picture for this approximation and compute the slope