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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization convex/concave functions
  5. Functions of one variable
  6. Infection point
  7. Exercise 1

Exercise 1

Which of the following functions has an inflection point on the interval $[-2,2]$?
$y(x)=x^3+1$
$y(x)=e^x+5$
$y(x)=x^2+3$
$y(x)=2x^3-15x^2$
Which of the following functions has an inflection point on the interval $[-2,2]$?
Antwoord 1 correct
Correct
Antwoord 2 optie
$y(x)=e^x+5$
Antwoord 2 correct
Fout
Antwoord 3 optie
$y(x)=x^2+3$
Antwoord 3 correct
Fout
Antwoord 4 optie
$y(x)=2x^3-15x^2$
Antwoord 4 correct
Fout
Antwoord 1 optie
$y(x)=x^3+1$
Antwoord 1 feedback
Correct: $y''(x)=6x$. Then $y''(0)=0$, $y''(x)>0$ for all $x>0$ and $y''(x)<0$ for all $x<0$. Hence, $x=0$ is an inflection point on the interval $[-2,2]$.

Go on.
Antwoord 2 feedback
Wrong: $y''(x)=e^x$, and hence, $y''(x)>0$ on the interval $[-2,2]$.

Try again.
Antwoord 3 feedback
Wrong: $y''(x)=2$ and hence, $y''(x)>0$ on the interval $[-2,2]$.

Try again.
Antwoord 4 feedback
Wrong: The function has indeed an inflection point for $x=2\frac{1}{2}$, but this point is not on the interval $[-2,2]$.

Try again.