Exercise 2 | Wiskunde op Tilburg University

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.