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1. Obtain the analytic value of the derivative of the function below at x = 0.50. ƒ(x) = −0.10x¹ – 0. 15x³ – 0. 50x² − 0. 25x + 1. 2 2. Obtain the derivative of the function at x = 0.50 using forward, backward and central finite difference methods using a step size h = 0.25. Compare your results to determine which finite difference gives the closest value to your answer in (1). 3. Obtain the derivative of the function at x = 0.50 using the improved forward-finite difference approximation. 4. Obtain the percent errors of the numerical derivatives in (2) and in (3) from the analytic value in (1).

1. Obtain the analytic value of the derivative of the function below at x = 0.50. ƒ(x) = −0.10x¹ – 0. 15x³ – 0. 50x² − 0. 25x + 1. 2 2. Obtain the derivative of the function at x = 0.50 using forward, backward and central finite difference methods using a step size h = 0.25. Compare your results to determine which finite difference gives the closest value to your answer in (1). 3. Obtain the derivative of the function at x = 0.50 using the improved forward-finite difference approximation. 4. Obtain the percent errors of the numerical derivatives in (2) and in (3) from the analytic value in (1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Obtain the analytic value of the derivative of the function below at x = 0.50. f(x) = −0.10x¹ – 0.15x³ – 0.50x² -0.25x + 1.2 2. Obtain the derivative of the function at x = 0.50 using forward, backward and central finite difference methods using a step size h = 0.25. Compare your results to determine which finite difference gives the closest value to your answer in (1). 3. Obtain the derivative of the function at x = 0.50 using the improved forward-finite difference approximation. 4. Obtain the percent errors of the numerical derivatives in (2) and in (3) from the analytic value in (1).
Transcribed Image Text:1. Obtain the analytic value of the derivative of the function below at x = 0.50. f(x) = −0.10x¹ – 0.15x³ – 0.50x² -0.25x + 1.2 2. Obtain the derivative of the function at x = 0.50 using forward, backward and central finite difference methods using a step size h = 0.25. Compare your results to determine which finite difference gives the closest value to your answer in (1). 3. Obtain the derivative of the function at x = 0.50 using the improved forward-finite difference approximation. 4. Obtain the percent errors of the numerical derivatives in (2) and in (3) from the analytic value in (1).
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