Exercise 4 | Wiskunde op Tilburg University

Determine all the extrema of

$f(x)=(x-2)^3$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$f(2)=0$ is a maximum.

Antwoord 2 correct

Fout

Antwoord 3 optie

$f(2)=0$ is a minimum.

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=2$ is a maximum.

Antwoord 4 correct

Fout

Antwoord 1 optie

There are no extrema.

Antwoord 1 feedback

Correct:

$f'(x)=3(x-2)^2$ . Hence,

$f'(x)=0$ if

$x=2$ . Via a sign chart (with for instance

$f'(0)=12$ and

$f'(4)=12$ ) we find that

$x=2$ is not an extremum location, but a saddle point. Hence, there are no extrema.

Go on.

Antwoord 2 feedback

Wrong: Not every stationary point is an extremum location.

See First-order condition extremum.

Antwoord 3 feedback

Wrong: Not every stationary point is an extremum location.

See First-order condition extremum.

Antwoord 4 feedback

Wrong: An extremum is never a value of the input variable.

Seee Minimum/maximum.