Problem 2: Consider the following function: I f(x) = -0.1x- 0.15x3 -0.5x2 -0.25x + 1.2 a....

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Problem 2: Consider the following function: I f(x) = -0.1x- 0.15x3 -0.5x2 -0.25x + 1.2 a. Use the Central Difference Method to estimate the first derivative of at x = 0.5. Start the computation at h = 1, then progressively divide the step size by a factor of 10 to demonstrate how the True Percent Error (roundoff error) becomes dominant as the step size is reduced. Plot the step size vs. the error. Hint: Use the loglog built-in function when plotting. Problem 2: Consider the following function: I f(x) = -0.1x- 0.15x3 -0.5x2 -0.25x + 1.2 a. Use the Central Difference Method to estimate the first derivative of at x = 0.5. Start the computation at h = 1, then progressively divide the step size by a factor of 10 to demonstrate how the True Percent Error (roundoff error) becomes dominant as the step size is reduced. Plot the step size vs. the error. Hint: Use the loglog built-in function when plotting.