Repeat Example 4.5, but for f (x) = cos(x) at x = /6.

Example 4.5

Problem Statement. In Example 4.4, we used a centered difference approximation of O(h) to estimate the first derivative of the following function at x = 0.5, f(x) = -0.1x4 -0.15x 0.5x 0.25x + 1.2 Perform the same computation starting with h = 1. Then progressively divide the step size by a factor of 10 to demonstrate how roundoff becomes dominant as the step size is reduced. Relate your results to Eq. (4.30). Recall that the true value of the derivative is -0.9125.