Chapter 4 – Quiz 1

1. Which of the following statements are true for any function f:X\mapsto\mathbb R when X\subseteq\mathbb R? (Multiple choice)

 
 
 
 
 
 

2. When can you be sure to have found the unique solution of an unconstrained maximization problem with objective f? (Multiple choice)

 
 
 
 
 

3. What is the global maximizer of f:\mathbb R\mapsto\mathbb R, x\mapsto x-x^2?

 
 
 
 
 
 

4. Suppose you are concerned with finding the global maximizer(s) in an unconstrained optimization problem with objective function f:X\mapsto\mathbb R that is twice differentiable. Which candidates x^* can not be ruled out as a potential solution by the first and second order conditions? (Multiple choice)

 
 
 
 

5. Select the requirements of the Weierstrass Extreme Value theorem, which together are a sufficient condition for existence of global extremizers in the unconstrained problem. (Multiple choice)

 
 
 
 
 
 
 

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