Exercise 1 | Wiskunde op Tilburg University

Determine all the extrema of the function

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

Antwoord 1 correct

Correct

Antwoord 2 optie

The function value

$y(0)=0$ is a minimum.

Antwoord 2 correct

Fout

Antwoord 3 optie

The function value

$y(0)=0$ is a maximum.

Antwoord 3 correct

Fout

Antwoord 4 optie

The function value

$y(1)=3$ is a maximum.

Antwoord 4 correct

Fout

Antwoord 1 optie

This function has no extrema.

Antwoord 1 feedback

Correct: Putting the first-order derivative

$y'(x)=3x^2+2$ equal to zero gives

$x^2=-\frac{2}{3}$ and this equation has no solution.

Go on.

Antwoord 2 feedback

Wrong: The point

$x=0$ is not a minimum location.

See saddle point.

Antwoord 3 feedback

Wrong: The point

$x=0$ is not a maximum location.

See saddle point.

Antwoord 4 feedback

Wrong: The function is convex on the interval

$(0,\infty)$ . Hence,

$x=1$ cannot be a maximum location.

See Convex and concave.