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Devoir22
@Devoir22
May 2019
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Bonsoir est ce que quelqu'un pourrait m'aider à trouver la question 2) a et b s'il vous plaît. Merci d'avance (niveau lycée)
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scoladan
Verified answer
Bonjour,
2) f(x) = x/2 + 11250/x
f'(x) = 1/2 - 11250/x²
⇔ f'(x) = (x² - 22500)/2x²
f'(x) = 0 sur [70;200]
⇒ x = √(22500) = 150
x 70 150 200
f'(x) - 0 +
f(x) décroissante croissante
f(x) est donc minimum pour x = 150
et f(150) = 150/2 + 11250/150 = 75 + 75 = 150
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Verified answer
Bonjour,2) f(x) = x/2 + 11250/x
f'(x) = 1/2 - 11250/x²
⇔ f'(x) = (x² - 22500)/2x²
f'(x) = 0 sur [70;200]
⇒ x = √(22500) = 150
x 70 150 200
f'(x) - 0 +
f(x) décroissante croissante
f(x) est donc minimum pour x = 150
et f(150) = 150/2 + 11250/150 = 75 + 75 = 150