Given the function: 5 4 2 f (x) = x^5 - 2x^4 + 3x^2- 1
a. Compute the exact derivative of f(x) at x = 2.1.
b. Estimate the first derivative of f(x) at x = 2.1 using a forward Taylor series approximation with the following step sizes: h [10^-4 10^-3 10^-2 10^-1 10^0 10^1 ]
Using the exact result from Part a, make a plot of the magnitude of the relative error in f '(x)x=2.1 versus step size -- use a log-log plot. From the plot or generated table (part b), determine the value of n (by hand calculation, or typed) in the error expression = h O(h ) . Explain!!!
c. Repeat Part b using a central Taylor series approximation for x f '(x)x=2.1 What is the “order of error” in this case? Plot the error vs. step size for this case in the same plot as above.