Exercise 1 | Wiskunde op Tilburg University

$f(x)=x^7+3x^2$ . Which of the following statements is true?

Antwoord 1 correct

Correct

Antwoord 2 optie

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

Antwoord 2 correct

Fout

Antwoord 3 optie

$x=0$ is a saddle point.

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=0$ is a maximum.

Antwoord 4 correct

Fout

Antwoord 1 optie

$x=0$ is a minimum location.

Antwoord 1 feedback

Correct:

$y'(x)=7x^6+6x$ . Hence,

$y'(0)=0$ .

$y''(x)=42x^5+6$ , which implies

$y''(0)=6>0$ . This means that

$x=0$ is a minimum location of

$f(x)$ .

Go on.

Antwoord 2 feedback

Wrong: What is

$f''(0)$ ?

See Second-order condition extremum.

Antwoord 3 feedback

Wrong: You need the second-order derivative in order to determine whether the stationary point is a minimum or a maximum.

See Second-order condition extremum.

Antwoord 4 feedback

Wrong: A maximum is always a function value.

See Minimum/maximum.