MSc Economics Preparatory Module

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

2. Consider the function . This function is:

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

4. Consider the function . This function is: (Hint: draw the function and consider the lower and upper level sets.)

5. Consider a function and suppose that is invertible. Further, consider a set and a value . 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 with domain and suppose that it is differentiable with derivative , and consider a point . Which statement about derivative concepts is false? (Single choice)

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