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Exercise 1: Reviewing High School Knowledge: Analytical Optimization

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Exercise 1: Reviewing High School Knowledge:

Analytical Optimization

Summer Term 2013

This exercise reviews some very fundamental optimization issues, which you have already stud- ied in school and during your first semesters.

Review: Review the terminology that we have discussed in the class:

1. Please, provide two different definitions of a maximum (and minimum, respectively):

2. What is the difference between a minimization and a maximization task?

To Do: Please, locate the optima of the following three one-dimensional functions. In so doing, discuss whether your solutions are minima or maxima. What are the particular character- istics and/or problems of the four functions?

Tasks: Please consider the following problems:

1. f(x) = 5x2−2x+ 10 2. g(x) = x3−6x2+ 12x−7 3. h(x) = (x2−8x+ 16)(x−1) 4. i(x) = sin(x)

Have fun, Ralf and Ralf.

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