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  2. For business economics
  3. Chapter 5: Optimization
  4. Optimization functions of one variable
  5. Monotonicity condition extremum
  6. Exercise 1

Exercise 1

Determine all extrema of $f(x)=x^2-3x+2$.
$f(1\frac{1}{2})=-\frac{1}{4}$ is a minimum
$f(1)=0$ is a maximum and $f(2)=0$ is a minimum
$f(1\frac{1}{2})=0$ is a minimum
$1\frac{1}{2}$ is a minimum
Determine all extrema of $f(x)=x^2-3x+2$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$f(1)=0$ is a maximum and $f(2)=0$ is a minimum
Antwoord 2 correct
Fout
Antwoord 3 optie
$f(1\frac{1}{2})=0$ is a minimum
Antwoord 3 correct
Fout
Antwoord 4 optie
$1\frac{1}{2}$ is a minimum
Antwoord 4 correct
Fout
Antwoord 1 optie
$f(1\frac{1}{2})=-\frac{1}{4}$ is a minimum
Antwoord 1 feedback
Correct: $y'(x)=2x-3$, hence $x=1\frac{1}{2}$ is a stationary point. Via a sign chart of $y'(x)$ we find that $x=1\frac{1}{2}$ is a minimum location. $y(1\frac{1}{2})=-\frac{1}{4}$.

Go on.
Antwoord 2 feedback
Wrong: A stationary point $c$ is not the zero of $y(x)$.

See Stationary point.
Antwoord 3 feedback
Wrong: You do not find the (value of an) extremum by plugging the stationary point into the derivative.

See Example (film).
Antwoord 4 feedback
Wrong: $x=1\frac{1}{2}$ is a minimum location.

See Example (film).