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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization convex/concave functions
  5. Functions of one variable
  6. Extrema
  7. Exercise 1

Exercise 1

Determine all the extrema of the function $y(x)=x^3+2x$.
This function has no extrema.
The function value $y(0)=0$ is a minimum.
The function value $y(0)=0$ is a maximum.
The function value $y(1)=3$ is a maximum.
Determine all the extrema of the function $y(x)=x^3+2x$.
Antwoord 1 correct
Correct
Antwoord 2 optie
The function value $y(0)=0$ is a minimum.
Antwoord 2 correct
Fout
Antwoord 3 optie
The function value $y(0)=0$ is a maximum.
Antwoord 3 correct
Fout
Antwoord 4 optie
The function value $y(1)=3$ is a maximum.
Antwoord 4 correct
Fout
Antwoord 1 optie
This function has no extrema.
Antwoord 1 feedback
Correct: Putting the first-order derivative $y'(x)=3x^2+2$ equal to zero gives $x^2=-\frac{2}{3}$ and this equation has no solution.

Go on.
Antwoord 2 feedback
Wrong: The point $x=0$ is not a minimum location.

See saddle point.
Antwoord 3 feedback
Wrong: The point $x=0$ is not a maximum location.

See saddle point.
Antwoord 4 feedback
Wrong: The function is convex on the interval $(0,\infty)$. Hence, $x=1$ cannot be a maximum location.

See Convex and concave.