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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of two variables
  5. Stationary point
  6. Exercise 3

Exercise 3

Determine all the stationary points of z(x,y)=13x3−x+13y3−4y.
(0,0)
There are no stationary points.
(1,2)
(−1,−2), (−1,2), (1,−2) and (1,2).
Determine all the stationary points of z(x,y)=13x3−x+13y3−4y.
Antwoord 1 correct
Correct
Antwoord 2 optie
(1,2)
Antwoord 2 correct
Fout
Antwoord 3 optie
(0,0)
Antwoord 3 correct
Fout
Antwoord 4 optie
There are no stationary points.
Antwoord 4 correct
Fout
Antwoord 1 optie
(−1,−2), (−1,2), (1,−2) and (1,2).
Antwoord 1 feedback
Correct:
  • z′x(x,y)=x2−1
  • z′y(x,y)=y2−4
z′x(x,y)=0 gives x=1 or x=−1.
z′y(x,y)=0 gives y=2 or y=−2.

This results in the four combinations.

Go on.
Antwoord 2 feedback
Wrong: Do not forget the negative solutions of a quadratic equation.

Try again.
Antwoord 3 feedback
Wrong: A stationary point is not a point where the function is equal to zero.

See Stationary point.
Antwoord 4 feedback
Wrong: What are the two partial derivatives?

Try again.