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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of one variable
  5. Monotonicity and derivative
  6. Exercise 3

Exercise 3

Determine all $x$ such that the function $h(x)=x^2+5\cdot\textrm{ln}(x)$ is decreasing.
For no $x$.
$x<0$
For all $x$.
$x\geq 0$
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.