Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 15, Problem 14P
Develop an M-file that is express ly designed to locate a maximum with the golden-section search algorithm. In other words, set it up so that it directly finds the maximum rather than finding the minimum of
• Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations.
• Return both the optimal x and
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Find the optimum of f(x) = 2.2x – 1.7x2 + x3 – 0.25x4
Perform: (Round-off all computed values to 4 decimal places.)a) (2 iterations) Golden-Section Search using XL = –2.4 and XU = 4.5
For each iteration, show the following: d, X1, X2, decision rule, ea, and the next XL andXU
Are you approaching a local or global optimum? ____________
Are you approaching a minimum or maximum optimum? __________
If the above graph is the graph of f′(x), then f(x) has a local maximum at x=___, a local minimum at x=____
and a critical point that is neither a local maximum nor a local minimum at x=____
Show that 5 is a critical number of the function
g(x) = 2+ (x -5)3but g does not have a local extremevalue at 5.
Chapter 15 Solutions
Numerical Methods for Engineers
Ch. 15 - A company makes two types of products, A and B....Ch. 15 - Prob. 2PCh. 15 - 15.3 Consider the linear programming...Ch. 15 - 15.4 Consider the linear programming...Ch. 15 - Use a software package (for example, Excel,...Ch. 15 - 15.6 Use a software package (for example, Excel,...Ch. 15 - 15.7 Consider the following constrained nonlinear...Ch. 15 - Use a software package to determine the maximum of...Ch. 15 - Use a software package to determine the maximum of...Ch. 15 - Given the following function,...
Ch. 15 - You are asked to design a covered conical pit to...Ch. 15 - 15.12 An automobile company has two versions of...Ch. 15 - 15.13 Og is the leader of the surprisingly...Ch. 15 - 15.14 Develop an M-file that is expressly designed...Ch. 15 - 15.15 Develop an M-file to locate a minimum with...Ch. 15 - Develop an M-file to implement parabolic...Ch. 15 - 15.17 The length of the longest ladder that can...
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