Exercise 4 | Wiskunde op Tilburg University

Determine

$a$ such that

$y(x)=x^2+(a-3)x+7$ is decreasing for

$x\leq 1$ and increasing for

$x\geq 1$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$a=-2$

Antwoord 2 correct

Fout

Antwoord 3 optie

$a=-1$

Antwoord 3 correct

Fout

Antwoord 4 optie

$a=2$

Antwoord 4 correct

Fout

Antwoord 1 optie

$a=1$

Antwoord 1 feedback

Correct:

$y'(x)=2x+a-3=0$ means

$x=\dfrac{3-a}{2}$ . For

$x=1$ there ia a change from decreasing to increasing. Hence,

$1=\dfrac{3-a}{2}$ , which implies that

$a=1$ . This means that

$y'(x)=2x-2$ and that

$y'(x)\leq 0$ for

$x\leq 1$ and

$y'(x)\geq 0$ for

$x\geq 1$ .

Go on.

Antwoord 2 feedback

Wrong:

$y'(x)\neq 2x+a$ .

See Derivative.

Antwoord 3 feedback

Wrong: Pay attention to the minus-signs.

Try again.

Antwoord 4 feedback

Wrong: Pay attention to the minus-signs.

Try again.