$f(x)=x^7+3x^2$. 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.
Go on.
Antwoord 2 feedback
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.
See Second-order condition extremum.
Antwoord 4 feedback