Error Sensitivity in Numerical Differentiation
Which of the following correctly ranks the given differentiation methods from least sensitive to most sensitive to measurement error?
I. Analytic differentiation
II. Secant method approximation with h = 1
III. Secant method approximation with h = 0.1
IV. Secant method approximation with h = 0.001
A
Secant with h = 0.001, Secant with h = 0.1, Secant with h = 1, Analytic differentiation
B
Analytic differentiation, Secant with h = 1, Secant with h = 0.1, Secant with h = 0.001
C
Secant with h = 1, Secant with h = 0.1, Analytic differentiation, Secant with h = 0.001
D
Secant with h = 0.1, Secant with h = 0.001, Analytic differentiation, Secant with h = 1
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