Using a Taylor series approximation, various finite difference methods can be derived. These methods are used to approximate the derivatives of functions at any point, . The three main types of finite difference methods are: The Forward Difference Method: The Backward Difference Method: The Central Difference Method: 2h The error due to these approximations can be given as the difference between the actual value of the derivative and our approximated value Assignment: This problem explores the trade-off between the truncation error in the finite difference approximation of the derivative and floating point truncation error incurred when using finite precision arithmetic (a) Write a MATLAB script that computes the forward finite difference ap- proximation of the derivative of sin(7x) for x 3. Use step sizes ranging from 10-1 to 10-16. The logspace command may be useful here. Plot the error, using a log-log scale, between your approximation and the exact derivative for each of your step sizes. (b) Based on your plot, what is the best step size to use for the finite difference step size? (c) Explain the behavior you see in the graph