Exercise 2 | Wiskunde op Tilburg University

Determine all the extrema locations of the function

$y(x)=e^{2x}-6x$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$x=0$ is a minimum location.

Antwoord 2 correct

Fout

Antwoord 3 optie

$x=0$ is a maximum location.

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=2-\ln{6}$ is a maximum location.

Antwoord 4 correct

Fout

Antwoord 1 optie

$x=\frac{1}{2}\ln{3}$ is a minimum location.

Antwoord 1 feedback

Correct: Putting the first-order derivative

$y'(x)=2e^{2x}-6$ equal to zero gives

$e^{2x}=3\Rightarrow 2x=\ln{3}\Rightarrow x=\frac{1}{2}\ln{3}$ . Moreover,

$y''(x)=4e^{2x}>0$ for all

$x$ . Hence, the function

$y(x)$ is convex, and hence

$x=\frac{1}{2}\ln{3}$ is a minimum location.

Go on.

Antwoord 2 feedback

Wrong:

$x=0$ is not a stationary point.

See Stationary point.

Antwoord 3 feedback

Wrong:

$x=0$ is not a stationary point.

See Stationary point.

Antwoord 4 feedback

Wrong:

$x=2-\ln{6}$ is not a stationary point.

See Stationary point.