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Title: Maths exercices
Description: some Maths exercices of Derivability and Fonctions :)
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SΓ©rie 4

Prof :AB
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π‘Ž) π‘€π‘œπ‘›π‘‘π‘Ÿπ‘’π‘Ÿ π‘žπ‘’π‘’ 𝑓 𝑒𝑠𝑑 π‘‘Γ©π‘Ÿπ‘–π‘£π‘Žπ‘π‘™π‘’ 𝑒𝑛 0 𝑝𝑒𝑖𝑠 π‘π‘Žπ‘™π‘π‘’π‘™π‘’π‘Ÿ 𝑓 β€² (0)
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2) π‘†π‘œπ‘–π‘‘ 𝑔(π‘₯) = √π‘₯ βˆ’ 3

πΈπ‘‘π‘’π‘‘π‘–π‘’π‘Ÿ π‘™π‘Ž π‘‘Γ©π‘Ÿπ‘–π‘£π‘Žπ‘π‘–π‘™π‘–π‘‘Γ© 𝑑𝑒 𝑔 Γ  π‘‘π‘Ÿπ‘œπ‘–π‘‘π‘’ 𝑑𝑒 3 𝑝𝑒𝑖𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘Ÿπ‘’π‘‘π‘’π‘Ÿ π‘”π‘Ÿπ‘Žπ‘β„Žπ‘–π‘žπ‘’π‘’π‘šπ‘’π‘›π‘‘ 𝑙𝑒 π‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘‘

3) π‘ π‘œπ‘–π‘‘ β„Ž (π‘₯) = |2π‘₯ βˆ’ 4|

πΈπ‘‘π‘’π‘‘π‘–π‘’π‘Ÿ π‘™π‘Ž π‘‘Γ©π‘Ÿπ‘–π‘£π‘Žπ‘π‘–π‘™π‘–π‘‘Γ© 𝑑𝑒 β„ŽΓ  π‘”π‘Žπ‘’π‘β„Žπ‘’ 𝑒𝑑 Γ  π‘‘π‘Ÿπ‘œπ‘–π‘‘π‘’ 𝑑𝑒 2 𝑝𝑒𝑖𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘Ÿπ‘’π‘‘π‘’π‘Ÿ π‘”π‘Ÿπ‘Žπ‘β„Žπ‘–π‘žπ‘’π‘’π‘šπ‘’π‘›π‘‘

𝑙𝑒 π‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘‘ π‘œπ‘π‘‘π‘’π‘›π‘’π‘’
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𝑑) 𝑓(π‘₯) = (π‘₯ 2 + 4π‘₯ βˆ’ 5)6

𝑔) 𝑓(π‘₯) = 2π‘₯ + οΏ½ π‘₯ 2 βˆ’ 1

a) π·π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿ 𝑙𝑒 π‘‘π‘Žπ‘π‘™π‘’π‘Žπ‘’ 𝑑𝑒 π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘‘π‘–π‘œπ‘› 𝑑𝑒 𝑓
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2) π‘†π‘œπ‘–π‘‘ 𝑔 𝑒𝑛𝑒 π‘“π‘œπ‘›π‘π‘‘π‘–π‘œπ‘› 𝑑é𝑓𝑖𝑛𝑖𝑒 π‘π‘Žπ‘Ÿ 𝑔(π‘₯) = π‘₯ 3 βˆ’ 3π‘₯ 2 + 6
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b) π·Γ©π‘‘π‘’π‘–π‘Ÿπ‘’ 𝑒𝑛 π‘’π‘›π‘π‘Žπ‘‘π‘Ÿπ‘’π‘šπ‘’π‘›π‘‘ 𝑑𝑒 √1
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π‘€π‘œπ‘›π‘‘π‘Ÿπ‘’π‘Ÿ π‘žπ‘’π‘’ π‘π‘œπ‘’π‘Ÿ π‘‘π‘œπ‘’π‘‘ π‘₯ 𝑑𝑒 οΏ½0, 4 οΏ½ π‘œπ‘› π‘Ž π‘₯ ≀ 𝑔(π‘₯) ≀ 2π‘₯
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Exercice nΒ°6:

π‘†π‘œπ‘–π‘‘ 𝑓 𝑒𝑛𝑒 π‘“π‘œπ‘›π‘π‘‘π‘–π‘œπ‘› 𝑑é𝑓𝑖𝑛𝑖𝑒 π‘ π‘’π‘Ÿ ]1, +∞[ π‘π‘Žπ‘Ÿ 𝑓(π‘₯) = 1 +

1) πΈπ‘‘π‘’π‘‘π‘–π‘’π‘Ÿ π‘™π‘Ž π‘‘Γ©π‘Ÿπ‘–π‘£π‘Žπ‘π‘–π‘™π‘–π‘‘Γ© 𝑑𝑒 𝑓 𝑒𝑑 π‘π‘Žπ‘™π‘π‘’π‘™π‘’π‘Ÿ π‘ π‘Ž π‘‘Γ©π‘Ÿπ‘–π‘£Γ©
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1

√π‘₯

3)π·Γ©π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘’π‘Ÿ 𝑙 β€² Γ©π‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 𝑑𝑒 π‘™π‘Ž π‘‘π‘Žπ‘›π‘”π‘’π‘›π‘‘π‘’ βˆ† Γ  𝐢𝑓 π‘Žπ‘’ π‘π‘œπ‘–π‘›π‘‘ 𝑑 β€² π‘Žπ‘π‘π‘–π‘ π‘ π‘’ π‘₯ = 2
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5) π‘€π‘œπ‘›π‘‘π‘Ÿπ‘’π‘Ÿ π‘žπ‘’π‘’ π‘π‘œπ‘’π‘Ÿ π‘‘π‘œπ‘’π‘‘ π‘₯ 𝑑𝑒 ]1, +∞[ ; |𝑓 β€² (π‘₯)| ≀

1
2


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𝑏)π·π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿ 𝑙𝑒 π‘‘π‘Žπ‘π‘™π‘’π‘Žπ‘’ 𝑑𝑒 π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘‘π‘–π‘œπ‘› 𝑑𝑒 𝑓
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3) π·Γ©π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘’π‘Ÿ 𝑙 β€² Γ©π‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 𝑑𝑒 π‘™π‘Ž π‘‘π‘Žπ‘›π‘”π‘’π‘›π‘‘π‘’ Γ  𝐢𝑓 π‘Žπ‘’ π‘π‘œπ‘–π‘›π‘‘ 𝑑 β€² π‘Žπ‘π‘ π‘π‘–π‘ π‘ π‘’ π‘₯ =

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Title: Maths exercices
Description: some Maths exercices of Derivability and Fonctions :)
Buy These NotesPreview