Chapter 3 – Quiz 1

1. What does the univariate derivative of a function f, evaluated at a point x_0 in the domain of f, express?

 
 
 
 

2. Consider the function f:\mathbb R\mapsto\mathbb R, x\mapsto 2x + 4. This function is:

 
 
 
 

3. What is not true about Taylor’s theorem and its statement about a function f around a point x_0?

 
 
 
 

4. Consider the function f:\mathbb R\mapsto\mathbb R, x\mapsto\max\{x,-2\} + 1. This function is: (Hint: draw the function and consider the lower and upper level sets.)

 
 
 
 

5. Consider a function f:X\mapsto Y and suppose that f is invertible. Further, consider a set B\subseteq Y and a value b\in Y. Which of the following relationships are certainly true? (Multiple choice)

 
 
 
 
 
 
 
 

6. What can you say about the concepts of (quasi-)convexity and concavity? (Multiple choice)

 
 
 
 
 
 

7. Consider a univariate, real-valued function f with domain X = \mathbb R and suppose that it is differentiable with derivative f', and consider a point x\in\mathbb R. Which statement about derivative concepts is false? (Single choice)

 
 
 
 

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