Q1. Which of the following is NOT required for using Newton’s method for optimization? The lower bound for search region. Twice differentiable optimization function. The function to be optimized. A good initial estimate that is reasonably close to the optimal. Q2. Which of the following statements is INCORRECT? If the second derivative at x_{i} is negative, then x_{i} is a maximum. If the first derivative at x_{i} is zero, then x_{i} is an optimum. If x_{i} is a minimum, then the second derivative at x_{i} is positive The value of the function can be positive or negative as any optima. Q3. For what value of x, is the function x^{2}2x6minimized? 0
1 Q4. We need to enclose a field with a fence. We have 500 feet of fencing material with a building on one side of the field where we will not need any fencing. Determine the maximum area of the field that can be enclosed by the fence. x=125, y=250 x=150, y=200 x=125, y=100 x=200, y=150 Q5. A rectangular box with a square base and no top has a volume of 500 cubic inches. Find the length, l of the edge of the square base and height, h for the box that requires the least amount of material to build. Conduct two iterations using an initial guess of l=5 in Base edge length is 10.00 and height is 5.00 Base edge length is 9.17 and height is 6.00 Base edge length is 9.00 and height is 6.17 Base edge length is 10.00 and height is 10.00 Q6. A rectangular box with a square base with no top has a surface area of 108 ft^{2}. Find the dimensions that will maximize the volume. Conduct two iterations using an initial guess of l=3 ft Base edge length is 4.15 and height is 4.85 Base edge length is 6.15 and height is 2.85 Base edge length is 6.00 and height is 3.00 Base edge length is 3.85 and height is 6.15

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 336205350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624, 0836981, 0836916, 0836805, 1322586. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Other sponsors include Maple, MathCAD, USF, FAMU and MSOE. Based on a work at http://mathforcollege.com/nm. Holistic Numerical Methods licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. 
