Exercise 3 | Wiskunde op Tilburg University

Determine all the extrema of

$y(x)=(5x-1)e^{4x}$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

There are no extrema.

Antwoord 2 correct

Fout

Antwoord 3 optie

$y(\frac{1}{5})=0$ is a maximum.

Antwoord 3 correct

Fout

Antwoord 4 optie

The correct answer is not among the other options.

Antwoord 4 correct

Fout

Antwoord 1 optie

$y(-\frac{1}{20})=-1\frac{1}{4}e^{-\frac{1}{5}}$ is a minimum

Antwoord 1 feedback

Correct:

$y'(x)=(20x+1)e^{4x}$ . Hence, the stationary point is

$x=-\frac{1}{20}$ .

$y''(x)=(80x+24)e^{4x}$ . Consequently,

$y''(-\frac{1}{20})=20e^{-\frac{1}{5}}>0$ and hence,

$y(-\frac{1}{20})=-1\frac{1}{4}e^{-\frac{1}{5}}$ is a minimum.

Go on.

Antwoord 2 feedback

Wrong:

$y'(x)=5e^{4x}+(5x-1)\cdot e^{4x} \cdot 4$ .

See Chain rule.

Antwoord 3 feedback

Wrong:

$y'(x)=5e^{4x}+(5x-1)\cdot e^{4x} \cdot 4$ .

See Chain rule.

Antwoord 4 feedback

Wrong: The correct answer is among them.

Try again.