Exercise 1 | Wiskunde op Tilburg University

Determine all values of

$x$ such that the function

$y(x)=-x^2+4x-3$ is decreasing.

Antwoord 1 correct

Correct

Antwoord 2 optie

$x>2$

Antwoord 2 correct

Fout

Antwoord 3 optie

$x<-2$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x<2$

Antwoord 4 correct

Fout

Antwoord 1 optie

$x \geq 2$

Antwoord 1 feedback

Correct:

$y'(x)=-2x+4$ . Hence,

$y'(x)=0$ if

$x=2$ .

Moreover,

$y'(x) \leq 0$ if

$x\geq 2$ . Hence,

$y(x)$ is decreasing if

$x \geq 2$ .

Go on.

Antwoord 2 feedback

Wrong: Decreasing is defined non-strictly.

See Monotonicity.

Antwoord 3 feedback

Wrong: What is the solution to

$-2x+4=0$ ?

Try again.

Antwoord 4 feedback

Wrong: For

$x<2$ it holds that

$y'(x)>0$ .

Try again.