Math Problem Statement
Réponse
Solution
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Question/Devoir
Énoncé :
- Soit la fonction définie sur par .
a. Étudier la dérivabilité de sur puis déterminer sa dérivée .
b. Montrer que la droite d'équation est asymptote à la courbe représentative de dans le repère orthonormé .
c. Étudier la position relative de et .
d. Établir le tableau de variations de .
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Related Questions:
- How do you determine if a function is differentiable over an interval?
- What are the steps to calculate the derivative of a rational function like ?
- How do you identify asymptotes of a function?
- How can you compare two functions to study their relative positions graphically?
- How do you construct a table of variations for a function?
Tip:
The asymptote suggests analyzing the behavior of as . Simplifying the terms helps to identify this asymptotic line.
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Math Problem Analysis
Mathematical Concepts
Differentiability
Derivatives
Asymptotes
Position of Functions
Function Variations
Formulas
Derivative of x → f'(x) = 1 - 2/x²
Asymptotic behavior as x → +∞: f(x) ≈ x - 2
Relative position of f(x) and y = x - 2
Theorems
Rules of Differentiation
Asymptote Determination
Behavior of Functions at Infinity
Suitable Grade Level
Grades 11-12 (High School)
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