Exercise 2 | Wiskunde op Tilburg University

Determine all the exterem of

$y(x)=2x-12$ ,

$0 \leq x \leq 10$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

There are no extrema.

Antwoord 2 correct

Fout

Antwoord 3 optie

$y(6)=0$ is a minimum.

Antwoord 3 correct

Fout

Antwoord 4 optie

Antwoord 4 correct

Fout

Antwoord 1 optie

The correct answer is not among the other options.

Antwoord 1 feedback

Correct:

$y'(x)=2$ . Hence,

$y'(x)$ has no zeros, which implies that

$y(x)$ has no stationary points. Consequently, the only extrema can be found at the boundary:

$y(0)=-12$ is a minimum and

$y(10)=8$ is a maximum.

Go on.

Antwoord 2 feedback

Wrong: Do not forget the boundary points.

See First-order condition extremum.

Antwoord 3 feedback

Wrong: A stationary point is not a zero of the function.

See Stationary point.

Antwoord 4 feedback

Wrong: A stationary point is not a zero of the function.

See Stationary point.