Question: A four-point formula for the derivative is Apply it to f(x) = x 4 with x 1 , · · ·, x 4 as in

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'₂from (14a), (14b), (14c), (15). Determine the errors. Compare and comment.

(-2f1 3f2 + 6f3 fa). f2 6h

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