Question: Derive the formula in Prob. 29 from (14) Data from Prob. 29 The derivative f'(x) can also be approximated in terms of first-order and higher

Derive the formula in Prob. 29 from (14)

Data from Prob. 29

The derivative f'(x) can also be approximated in terms of first-order and higher order differences.

(4fo-% f'(xo) - I,v² - %v +

Compute f'(0.4) in Prob. 27 from this formula, using differences up to and including first order, second order, third order, fourth order.

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.

(4fo-% f'(xo) - I,v - %v +

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