the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number…

the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\no 20\no 60\no 80\no 100

the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\no 20\no 60\no 80\no 100

Answer

Explanation:

Step1: Écrire la fonction au format standard

On développe $f(x)=-(x - 20)(x - 100)=-(x^{2}-100x-20x + 2000)=-x^{2}+120x - 2000$.

Step2: Identifier les coefficients

Pour une fonction quadratique $y = ax^{2}+bx + c$, ici $a=-1$, $b = 120$, $c=-2000$.

Step3: Trouver l'abscisse du sommet

L'abscisse du sommet d'une fonction quadratique $y = ax^{2}+bx + c$ est donnée par $x=-\frac{b}{2a}$. On remplace $a$ et $b$ : $x=-\frac{120}{2\times(-1)}=\frac{-120}{-2}=60$.

Answer:

B. 60