Exercise 1 | Wiskunde op Tilburg University

Determine all extrema of

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

Antwoord 1 correct

Correct

Antwoord 2 optie

$f(1)=0$ is a maximum and

$f(2)=0$ is a minimum

Antwoord 2 correct

Fout

Antwoord 3 optie

$f(1\frac{1}{2})=0$ is a minimum

Antwoord 3 correct

Fout

Antwoord 4 optie

$1\frac{1}{2}$ is a minimum

Antwoord 4 correct

Fout

Antwoord 1 optie

$f(1\frac{1}{2})=-\frac{1}{4}$ is a minimum

Antwoord 1 feedback

Correct:

$y'(x)=2x-3$ , hence

$x=1\frac{1}{2}$ is a stationary point. Via a sign chart of

$y'(x)$ we find that

$x=1\frac{1}{2}$ is a minimum location.

$y(1\frac{1}{2})=-\frac{1}{4}$ .

Go on.

Antwoord 2 feedback

Wrong: A stationary point

$c$ is not the zero of

$y(x)$ .

See Stationary point.

Antwoord 3 feedback

Wrong: You do not find the (value of an) extremum by plugging the stationary point into the derivative.

See Example (film).

Antwoord 4 feedback

Wrong:

$x=1\frac{1}{2}$ is a minimum location.

See Example (film).