Exercise 3 | Wiskunde op Tilburg University

Determine all

$x$ such that the function

$h(x)=x^2+5\cdot\textrm{ln}(x)$ is decreasing.

Antwoord 1 correct

Correct

Antwoord 2 optie

$x<0$

Antwoord 2 correct

Fout

Antwoord 3 optie

For all

$x$ .

Antwoord 3 correct

Fout

Antwoord 4 optie

$x\geq 0$

Antwoord 4 correct

Fout

Antwoord 1 optie

For no

$x$ .

Antwoord 1 feedback

Correct: The domain of

$h(x)$ is

$x>0$ and

$h'(x)=2x+\dfrac{5}{x}\geq 0$ for all

$x>0$ .

Go on.

Antwoord 2 feedback

Wrong: Pay attention to the domain of a logarithmic function.

See Logarithmic functions.

Antwoord 3 feedback

Wrong: Note that

$h'(x)\leq 0$ has to hold.

See Monotonicity and derivative.

Antwoord 4 feedback

Wrong: Note that

$h'(x)\leq 0$ has to hold.

See Monotonicity and derivative.