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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization convex/concave functions
  5. Functions of two variables
  6. Second-order condition
  7. Exercise 1

Exercise 1

Which of the following statements is true for the function $z(x,y)=e^{2x}+e^y$.
The function is convex.
The function is concave.
The function is convex on the interval $(-\infty,0]$ and concave on the interval $[0,\infty]$.
The function is neither convex nor concave.
Which of the following statements is true for the function $z(x,y)=e^{2x}+e^y$.
Antwoord 1 correct
Correct
Antwoord 2 optie
The function is concave.
Antwoord 2 correct
Fout
Antwoord 3 optie
The function is convex on the interval $(-\infty,0]$ and concave on the interval $[0,\infty]$.
Antwoord 3 correct
Fout
Antwoord 4 optie
The function is neither convex nor concave.
Antwoord 4 correct
Fout
Antwoord 1 optie
The function is convex.
Antwoord 1 feedback
Correct: The criterion function $C(x,y)=4e^{2x}e^{y}$ and the second-order partial derivatives $z''_{xx}(x,y)=4e^{2x}$ and $z''_{yy}(x,y)=e^{y}$ are positive for all values of $x$ and $y$.

Go on.
Antwoord 2 feedback
Wrong: When is a function concave?

See criterion function.
Antwoord 3 feedback
Wrong: Determine the criterion function and the second-order partial derivatives.

See criterion function.
Antwoord 4 feedback
Wrong: Determine the criterion function and the second-order partial derivatives.

See criterion function.