Numerical differentiation
General · Mathematics
Study notes
Q: Approximate f'(1) for f(x) = eˣ using h = 0.1: forward vs central. Forward: (e^1.1-e^1)/0.1 = (3.0042-2.7183)/0.1 = 2.859. Central: (e^1.1-e^0.9)/0.2 = (3.0042-2.4596)/0.2 = 2.723. True e = 2.71828: central (2.723) beats forward (2.859)! Central: O(h²) vs O(h)! (But h too small: round-off!)