Exercise 1 | Wiskunde op Tilburg University

Which of the following functions has an inflection point on the interval

$[-2,2]$ ?

Antwoord 1 correct

Correct

Antwoord 2 optie

$y(x)=e^x+5$

Antwoord 2 correct

Fout

Antwoord 3 optie

$y(x)=x^2+3$

Antwoord 3 correct

Fout

Antwoord 4 optie

$y(x)=2x^3-15x^2$

Antwoord 4 correct

Fout

Antwoord 1 optie

$y(x)=x^3+1$

Antwoord 1 feedback

Correct:

$y''(x)=6x$ . Then

$y''(0)=0$ ,

$y''(x)>0$ for all

$x>0$ and

$y''(x)<0$ for all

$x<0$ . Hence,

$x=0$ is an inflection point on the interval

$[-2,2]$ .

Go on.

Antwoord 2 feedback

Wrong:

$y''(x)=e^x$ , and hence,

$y''(x)>0$ on the interval

$[-2,2]$ .

Try again.

Antwoord 3 feedback

Wrong:

$y''(x)=2$ and hence,

$y''(x)>0$ on the interval

$[-2,2]$ .

Try again.

Antwoord 4 feedback

Wrong: The function has indeed an inflection point for

$x=2\frac{1}{2}$ , but this point is not on the interval

$[-2,2]$ .

Try again.