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

Exercise

The function $y(x)$ is defined on the interval $0\leq x$ and it is know that $y(x)$ has three stationary points. What do we know about the number of extrema of this function?
There are at most four.
There are four.
There are three.
There are at least four.
The function $y(x)$ is defined on the interval $0\leq x$ and it is know that $y(x)$ has three stationary points. What do we know about the number of extrema of this function?
Antwoord 1 correct
Correct
Antwoord 2 optie
There are four.
Antwoord 2 correct
Fout
Antwoord 3 optie
There are three.
Antwoord 3 correct
Fout
Antwoord 4 optie
There are at least four.
Antwoord 4 correct
Fout
Antwoord 1 optie
There are at most four.
Antwoord 1 feedback
Correct: The boundary point $x=0$ is certainly an extremum location. Moreover, each stationary point could be one as well.

Go on.
Antwoord 2 feedback
Wrong: Not every stationary point is an extremum location.

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

See First-order condition extremum.
Antwoord 4 feedback
Wrong: Each extremum location is either a boundary or a stationary point.

See First-order condition extremum.