We discussed the process of numerical differentiation using the approximation

Using the Taylor series for f(a + h) and f(a – h) about x = a, show that

to f´(a) with truncation error O(h⁶). Apply this extrapolation procedure to find f´(1) when f(x) = cosh x, taking h = 0.4, 0.2 and 0.1, working to as many decimal places as your calculator will permit.

Transcribed Image Text:

o(h) = f(a +h)-f(a - h) 2h