A calculator produced the following approximations for using central-difference…
MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A calculator produced the following approximations for p′(2) using central-difference slopes with different interval widths.
• h=0.2: 1.234
• h=0.1: 1.210
• h=0.01: 1.048
Each individual function value used in these computations has a round-off error no greater than 0.002. Which approximation is most likely to minimize the total error, and what value would you report for p′(2)? Give a brief justification.