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

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

Example 4.5

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Problem Statement. In Example 4.4, we used a centered difference approximation of O(h²) to estimate the first derivative of the following function at x = 0.5, f(x) = -0.1x4 -0.15x³ – 0.5x² – 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.