# Exercise 2

Determine all the extrema locations of the function $y(x)=e^{2x}-6x$.
$x=\frac{1}{2}\ln{3}$ is a minimum location.
$x=0$ is a minimum location.
$x=0$ is a maximum location.
$x=2-\ln{6}$ is a maximum location.
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.