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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of one variable
  5. Alternative monotonicity condition extremum
  6. Exercise 2

Exercise 2

Determine all the exterem of $y(x)=2x-12$, $0 \leq x \leq 10$.
The correct answer is not among the other options.
There are no extrema.
$y(6)=0$ is a minimum.
  • $y(6)=0$ is a minimum.
  • $y(0)=-12$ is a boundary minimum
  • $y(10)=8$ is a boundary maximum
Determine all the exterem of $y(x)=2x-12$, $0 \leq x \leq 10$.
Antwoord 1 correct
Correct
Antwoord 2 optie
There are no extrema.
Antwoord 2 correct
Fout
Antwoord 3 optie
$y(6)=0$ is a minimum.
Antwoord 3 correct
Fout
Antwoord 4 optie
  • $y(6)=0$ is a minimum.
  • $y(0)=-12$ is a boundary minimum
  • $y(10)=8$ is a boundary maximum
Antwoord 4 correct
Fout
Antwoord 1 optie
The correct answer is not among the other options.
Antwoord 1 feedback
Correct: $y'(x)=2$. Hence, $y'(x)$ has no zeros, which implies that $y(x)$ has no stationary points. Consequently, the only extrema can be found at the boundary: $y(0)=-12$ is a minimum and $y(10)=8$ is a maximum.

Go on.
Antwoord 2 feedback
Wrong: Do not forget the boundary points.

See First-order condition extremum.
Antwoord 3 feedback
Wrong: A stationary point is not a zero of the function.

See Stationary point.
Antwoord 4 feedback
Wrong: A stationary point is not a zero of the function.

See Stationary point.