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  3. Chapter 5: Optimization
  4. Optimization functions of two variables
  5. First-order condition extremum
  6. Exercise

Exercise

We know that the function $z(x,y)$, $(x,y\geq 0)$, has at least two stationary points. Which of the following statements is true?
There is at least one extremum.
There are at least two extrema.
There are at least three extrema.
All the other statements are incorrect.
We know that the function $z(x,y)$, $(x,y\geq 0)$, has at least two stationary points. Which of the following statements is true?
Antwoord 1 correct
Fout
Antwoord 2 optie
There are at least two extrema.
Antwoord 2 correct
Fout
Antwoord 3 optie
There are at least three extrema.
Antwoord 3 correct
Fout
Antwoord 4 optie
All the other statements are incorrect.
Antwoord 4 correct
Correct
Antwoord 1 optie
There is at least one extremum.
Antwoord 1 feedback
Wrong: Not every boundary point is an extremum location.

See First-order condition extremum.
Antwoord 2 feedback
Wrong: Not every stationary point is an extremum.

See First-order condition extremum.
Antwoord 3 feedback
Wrong: Not every stationary point is an extremum.

See First-order condition extremum.
Antwoord 4 feedback
Correct: Neither a stationary point nor a boundary point is always an extremum location.

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