Question

The following table of values of f(x) is given:
x →0.25 0.30 0.35
f(x)→1.25 1.90 1.68

Compute f'(x) at x=0.30 using an O(h²) formula.

Answer 1

two-point central difference formula for the first derivative of order O(h²):

$$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$$

$$f'(0.30)\approx\frac{f(0.35)-f(0.25)}{0.35-0.25}=\frac{1.68-1.25}{0.1}=4.3$$