A four-point formula for the derivative is Apply it to f(x) = x 4 with x 1

A €œfour-point formula€ for the derivative is

Apply it to f(x) = x⁴ with x₁, · · ·, x₄ as in Prob. 27, determine the error, and compare it with that in the case of (15).

Data from Prob. 27

Consider f(x) = x⁴ for x₀ = 0, x₁ = 0.2, x₂ = 0.4, x₃ = 0.6, x₄ = 0.8. Calculate f'₂ from (14a), (14b), (14c), (15). Determine the errors. Compare and comment.

Transcribed Image Text:

(-2f1 – 3f2 + 6f3 – fa). f2 6h