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f(x) = 5x² + 3x³ 08 06 044 1. Using the laws of Calculus, provide the expression for f"(x)- which will be our basis for analytical (theoretical comparison) 2. With x= -0.60, x= -0.55, x= -0.50, x= -0.45, x= -0.40, x= -0.35, x= -0.30, find f"(-0.45) using: a) 3-point Backward difference b) 3-point Forward Difference c) 3-point Central Difference d) 4-point Backward Difference 4-point Forward Difference e) f) 5-point Central Difference 3. Compute the relative error (%) for each method

f(x) = 5x² + 3x³ 08 06 044 1. Using the laws of Calculus, provide the expression for f"(x)- which will be our basis for analytical (theoretical comparison) 2. With x= -0.60, x= -0.55, x= -0.50, x= -0.45, x= -0.40, x= -0.35, x= -0.30, find f"(-0.45) using: a) 3-point Backward difference b) 3-point Forward Difference c) 3-point Central Difference d) 4-point Backward Difference 4-point Forward Difference e) f) 5-point Central Difference 3. Compute the relative error (%) for each method

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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Problem 2: Consider the function: 1. Using the laws of Calculus, provide the expression for f"(x)- which will be our basis for analytical (theoretical comparison) f(x) = 5x4 + 3x3 08 2. With x= - 0.60, x= - 0.55, x= - 0.50, x= - 0.45, x= - 0.40, x= - 0.35, x= - 0.30, find f"'(-0.45) using: a) 3-point Backward difference b) 3-point Forward Difference c) 3-point Central Difference d) 4-point Backward Difference e) 4-point Forward Difference f) 5-point Central Difference 04 02 3. Compute the relative error (%) for each method 02 Numerical Solution
Transcribed Image Text:Problem 2: Consider the function: 1. Using the laws of Calculus, provide the expression for f"(x)- which will be our basis for analytical (theoretical comparison) f(x) = 5x4 + 3x3 08 2. With x= - 0.60, x= - 0.55, x= - 0.50, x= - 0.45, x= - 0.40, x= - 0.35, x= - 0.30, find f"'(-0.45) using: a) 3-point Backward difference b) 3-point Forward Difference c) 3-point Central Difference d) 4-point Backward Difference e) 4-point Forward Difference f) 5-point Central Difference 04 02 3. Compute the relative error (%) for each method 02 Numerical Solution
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