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  3. Chapter 5: Optimization
  4. Optimization functions of two variables
  5. Minimum/maximum
  6. Exercise

Exercise

The function $z(x,y)=x^2+y^2$ has exactly one minimum. Determine that minimum.
$z(0,0)=0$.
$(x,y)=(0,0)$.
$z(-1,-1)=-2$.
$(x,y)=(-1,1)$.
The function $z(x,y)=x^2+y^2$ has exactly one minimum. Determine that minimum.
Antwoord 1 correct
Correct
Antwoord 2 optie
$(x,y)=(0,0)$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$z(-1,-1)=-2$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$(x,y)=(-1,1)$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$z(0,0)=0$.
Antwoord 1 feedback
Correct: $z(0,0)=0$ and $z(x,y)\geq 0$ for every other combination of $x$ and $y$. Hence, $z(0,0)=0$ is the minimum of the function.

Go on.
Antwoord 2 feedback
Wrong: Note the difference between a minimum and a minimum location.

See Minimum/maximum.
Antwoord 3 feedback
Wrong: $(-1)^2\neq -1$.

Try again.
Antwoord 4 feedback
Wrong: Note the difference between a minimum and a minimum location.

See Minimum/maximum.