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Consider the function f(x) = 4e – (x – 1)2 + e -4x2 – sin x. (a) Plot the function over a range that shows its maximum value. (b) You could find the x corresponding to the maximum function value by solving a root-finding problem F(x) = 0. Write the expression (by hand, though via code is OK) for this F(x). (c) Use Newton's Method (via code, though you might first need to take a derivative by hand) to find the x location of the maximum value to an absolute tolerance of 10 -6 (use a large enough max # iterations so that this tolerance is reached).

Consider the function f(x) = 4e – (x – 1)2 + e -4x2 – sin x. (a) Plot the function over a range that shows its maximum value. (b) You could find the x corresponding to the maximum function value by solving a root-finding problem F(x) = 0. Write the expression (by hand, though via code is OK) for this F(x). (c) Use Newton's Method (via code, though you might first need to take a derivative by hand) to find the x location of the maximum value to an absolute tolerance of 10 -6 (use a large enough max # iterations so that this tolerance is reached).

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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Consider the function f(x) = 4e – (x – 1)2 + e -4x2 – sin x. (a) Plot the function over a range that shows its maximum value. (b) You could find the x corresponding to the maximum function value by solving a root-finding problem F(x) = 0. Write the expression (by hand, though via code is OK) for this F(x). (c) Use Newton's Method (via code, though you might first need to take a derivative by hand) to find the x location of the %3D maximum value to an absolute tolerance of 10 -6 (use a large enough max # iterations so that this tolerance is reached).
Transcribed Image Text:Consider the function f(x) = 4e – (x – 1)2 + e -4x2 – sin x. (a) Plot the function over a range that shows its maximum value. (b) You could find the x corresponding to the maximum function value by solving a root-finding problem F(x) = 0. Write the expression (by hand, though via code is OK) for this F(x). (c) Use Newton's Method (via code, though you might first need to take a derivative by hand) to find the x location of the %3D maximum value to an absolute tolerance of 10 -6 (use a large enough max # iterations so that this tolerance is reached).
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