Exercise 2 | Wiskunde op Tilburg University

Determine all the extrema of

$y(x)=-x^3+5x^2+8x+5$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

Antwoord 2 correct

Fout

Antwoord 3 optie

Antwoord 3 correct

Fout

Antwoord 4 optie

Antwoord 4 correct

Fout

Antwoord 1 optie

Antwoord 1 feedback

Correct:

$y'(x)=-3x^2+10x+8$ .

$y'(x)=0$ gives

$x=-\frac{2}{3}$ and

$x=4$ .

$y''(x)=-6x+10$ . Since

$y''(-\frac{2}{3})=14>0$ it holds that

$y(-\frac{2}{3})=2\frac{5}{27}$ is a minimum, and since

$y''(4)=-14<0$ it holds that

$y(4)=53$ is a maximum.

Go on.

Antwoord 2 feedback

Wrong: The value of the extremum can be found by the use of the original function, not by the use of the second-order derivative.

Try again.

Antwoord 3 feedback

Wrong:

$y''(c)>0$ means that a stationary point

$c$ is a minimum location.

See Second-order condition extremum.

Antwoord 4 feedback

Wrong: The value of the extremum can be found by the use of the original function, not by the use of the second-order derivative.

Try again.