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Question 2 (i) - Verify Rolles theorem - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Verify Rolles theorem
Chapter 5 Class 12 Continuity and Differentiability
Concept wise
- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
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Verify Rolles theorem
- Verify Mean Value Theorem
Transcript
Question 2 Examine if Rolleโs theorem is applicable to the functions. Can you say some thing about the converse of Rolleโs theorem from this function? (๐) ๐ (๐ฅ) = [๐ฅ] ๐๐๐ ๐ฅ โ [5, 9]Greatest Integer less than equal to ๐ฅ ๐ (๐ฅ) =[๐ฅ] is not continuous & differentiable โ Condition of Rolleโs Theorem is not satisfied. Therefore, Rolleโs Theorem is not applicable .
