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Home » #### -1,89 m/s² - Silent Sales Machine

#### -1,89 m/s² - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 #### Largeur : 8 cm, Longueur : 16 cm

📌 Résoudre pour \(x\): \(\log_2(x) + \log_2(8) = 5\)

📌 Utiliser la propriété \(\log_b(m) + \log_b(n) = \log_b(mn)\) :

📌 \(8x = 2^5 = 32\)

📌 \(x = \frac{32}{8} = 4\)

📌 Le bénéfice d'une entreprise est modélisé par \(P(x) = -2x^2 + 40x - 50\), où \(x\) est le nombre d'unités vendues. Quel est le bénéfice maximal ?

📌 La fonction de bénéfice est une parabole orientée vers le bas. Le sommet donne le bénéfice maximal.

📌 Abscisse du sommet : \(x = -\frac{b}{2a} = -\frac{40}{2(-2)} = 10\)

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\frac{1}{u^2} + \frac{2}{u} + 1 + 2u
Define the function:
f(u) = \frac{1}{u^2} + \frac{2}{u} + 1 + 2u, \quad 0 < u \leq \frac{1}...
We now find the maximum of $f(u)$ on this interval. Note that as $u \t...
But wait: as $u \to 0^+$, $\frac{1}{u^2} \to \infty$, so $f(u) \to \in...
Let’s test at $x = \frac{\pi}{4}$: $\sin x = \cos x = \frac{\sqrt{2}}{...
So $u = \frac{1}{2}$ at $x = \frac{\pi}{4}$, and $f\left(\frac{1}{2}\r...
Now check the behavior as $u \to 0^+$:
\frac{1}{u^2} \to \infty, \quad \frac{2}{u} \to \infty, \quad 2u \to 0
So $f(u) \to \infty$

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