(a) Develop a first-order method for approximating f" (x) which uses the data f (x - 3h), f (x) and f (r+ h). (b) Use the three-point centred difference formula for the second derivative to ap- proximate f" (1), where f (x) = x-2, for h = 0.1, 0.01 and 0.001. Furthermore, determine the approximation error. Use an accuracy of 6 decimal digits for the final answers of the derivative values only.

(a) Develop a first-order method for approximating f" (x) which uses the data f (x - 3h), f (x) and f (r+ h). (b) Use the three-point centred difference formula for the second derivative to ap- proximate f" (1), where f (x) = x-2, for h = 0.1, 0.01 and 0.001. Furthermore, determine the approximation error. Use an accuracy of 6 decimal digits for the final answers of the derivative values only.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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