1. Home
  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization convex/concave functions
  5. Functions of two variables
  6. Extrema and saddle points
  7. Exercise 2

Exercise 2

Determine all the extremum locations of the function $z(x,y)=e^{2x}+e^y$.
The function has no extrema.
The point $(0,0)$ is a minimum location.
The point $(0,0)$ is a maximum location.
The point $(-1,-1)$ is a minimum location and the point $(1,1)$ is a maximum location.
Determine all the extremum locations of the function $z(x,y)=e^{2x}+e^y$.
Antwoord 1 correct
Correct
Antwoord 2 optie
The point $(0,0)$ is a minimum location.
Antwoord 2 correct
Fout
Antwoord 3 optie
The point $(0,0)$ is a maximum location.
Antwoord 3 correct
Fout
Antwoord 4 optie
The point $(-1,-1)$ is a minimum location and the point $(1,1)$ is a maximum location.
Antwoord 4 correct
Fout
Antwoord 1 optie
The function has no extrema.
Antwoord 1 feedback
Correct: The first-order partial derivatives are $z'_x(x,y)=2e^{2x}$ and $z'_y(x,y)=e^y$. No points $(x,y)$ exist such that $2e^{2x}=0$ and $e^y=0$.

Go on.
Antwoord 2 feedback
Wrong: Consider the first-order partial derivatives $z'_x(x,y)$ and $z'_y(x,y)$.

Try again.
Antwoord 3 feedback
Wrong: Consider the first-order partial derivatives $z'_x(x,y)$ and $z'_y(x,y)$.

Try again.
Antwoord 4 feedback
Wrong: Consider the first-order partial derivatives $z'_x(x,y)$ and $z'_y(x,y)$.

Try again.