''''''''''MATLAB"""""""""""

Use a centered difference approximation on the order of O(h) to estimate the second derivative of the function, f(x)=25x3-6x2 +7x-88. Perform the evaluation at x = 2 using first a step size of h = 0.25 and repeat with step size h = 0.125. Compare your two estimates with the true value of the second derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion. Problem 1.4: (Verify Chapra Example 4.8 with MATLAB) Create a MATLAB program that uses a centered divided difference approximation of O(h) to estimate the first derivative of the function, f(x)--0, 1x4-0.1 5x3-05x2-0.25x + 1 .2 at x = 0.5. Beginning with a step size of h = 1, progressively divide the step size by a factor of 10 until h-10"0. Create a log-log plot of the step size vs. the error. Why does the plot have this shape