Investigate the effect of using a smaller value for h in Example 8.37. Show that (0.1) gives

Investigate the effect of using a smaller value for h in Example 8.37. Show that Φ(0.1) gives a poorer estimate for f´(0.5) and the error bound for the consequent extrapolation [4Φ(0.1) – Φ(0.2)]/3 is 7 × 10^–4.

Data from Example 8.37.

Estimate f´(0.5), where f (x) is given by the table

Transcribed Image Text:

x 0.1 f(x) 0.0998 0.2 0.1987 0.4 0.3 0.2955 0.3894 0.5 0.4794 0.6 0.7 0.8 0.5646 0.6442 0.7174 0.9 0.7833