Exercise 2 | Wiskunde op Tilburg University

Consider the function

$y(x)=3x^2+e^{2x}$ on the interval

$x<0$ . Which of the following statements is true?

Antwoord 1 correct

Correct

Antwoord 2 optie

The function is concave.

Antwoord 2 correct

Fout

Antwoord 3 optie

The functions is neither convex nor concave.

Antwoord 3 correct

Fout

Antwoord 4 optie

None of the others statements are correct.

Antwoord 4 correct

Fout

Antwoord 1 optie

The function is convex

Antwoord 1 feedback

Correct: From

$y''(x)=6+4e^{2x}$ it follows that

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

$x<0$ . Hence, the function is convex.

Go on.

Antwoord 2 feedback

Wrong: Note that

$e^{2x}>0$ for every

$x$ , hence also for

$x<0$ .

Try again.

Antwoord 3 feedback

Wrong: Determine the second-order derivative

$y''(x)$ and use the second-order condition.

See second-order condition.

Antwoord 4 feedback

Wrong: Determine the second-order derivative

$y''(x)$ and use the second-order condition.

See second-order condition.