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

Exercise 4

Determine $a$ such that $y(x)=x^2+(a-3)x+7$ is decreasing for $x\leq 1$ and increasing for $x\geq 1$.
$a=1$
$a=-2$
$a=-1$
$a=2$
Determine $a$ such that $y(x)=x^2+(a-3)x+7$ is decreasing for $x\leq 1$ and increasing for $x\geq 1$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$a=-2$
Antwoord 2 correct
Fout
Antwoord 3 optie
$a=-1$
Antwoord 3 correct
Fout
Antwoord 4 optie
$a=2$
Antwoord 4 correct
Fout
Antwoord 1 optie
$a=1$
Antwoord 1 feedback
Correct: $y'(x)=2x+a-3=0$ means $x=\dfrac{3-a}{2}$. For $x=1$ there ia a change from decreasing to increasing. Hence, $1=\dfrac{3-a}{2}$, which implies that $a=1$. This means that $y'(x)=2x-2$ and that $y'(x)\leq 0$ for $x\leq 1$ and $y'(x)\geq 0$ for $x\geq 1$.

Go on.
Antwoord 2 feedback
Wrong: $y'(x)\neq 2x+a$.

See Derivative.
Antwoord 3 feedback
Wrong: Pay attention to the minus-signs.

Try again.
Antwoord 4 feedback
Wrong: Pay attention to the minus-signs.

Try again.