Lakshesh Verma Lakshesh Verma

Lecture 6 : Second Order Derivative & Mean Value Theorem

  • Chapter-5. Continuity and Differentiability Assignments 1

    Verify Mean Value Theorem, if in the interval [a, b], where a = 1 and b = 3. Find all for which 

     

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  • Chapter-5. Continuity and Differentiability Assignments 2

    Verify Mean Value Theorem, if  in the interval, where and.

     

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  • Chapter-5. Continuity and Differentiability Assignments 3

    If is a differentiable function and if does not vanish anywhere, then prove that.

     

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  • Chapter-5. Continuity and Differentiability Assignments 4

     

    Examine if Rolle's Theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's Theorem from these examples?

    (i) 

    (ii) 

    (iii) 

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  • Chapter-5. Continuity and Differentiability Assignments 5

    Verify Rolle's Theorem for the function

     

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  • Chapter-5. Continuity and Differentiability Assignments 6

      

    If, show that

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  • Chapter-5. Continuity and Differentiability Assignments 7

     

    If, show that

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  • Chapter-5. Continuity and Differentiability Assignments 8

      

    If, show that

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  • Chapter-5. Continuity and Differentiability Assignments 9


    Ifshow that

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  • Chapter-5. Continuity and Differentiability Assignments 10

     

    If, show that

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  • Chapter-5. Continuity and Differentiability Assignments 11

     

    If findin terms of y alone.

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  • Chapter-5. Continuity and Differentiability Assignments 12

      

    If, prove that

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  • Chapter-5. Continuity and Differentiability Assignments 13

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 14

      

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 15

      

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 16

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 17

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 18

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 19

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 20

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 21

     

    Find the second order derivatives of the function.

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  • Chapter-5. Continuity and Differentiability Assignments 22

     

    Find the second order derivatives of the function.

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    • Description:-

    Lecture 6:
    Today, we will discuss the last two topics, i.e; Second Order Derivative & Mean Value Theorem of Chapter 5 Continuity and Differentiability.
    Objectives:
    1. Basic concept about Second Order Derivative.
    2. Concept of Mean Value Theorem.
    Important Tip: 
    This lecture is about Second Order Derivative & Mean Value Theorem. In this topic, you’ll get to learn all about second order derivatives. You'll also get to know about Mean Value Theorem. Have a clear focus on these topics as it help you in further studies also.
    Please go through the topic, their notes. Properly do the assignments, watch videos of the concerned topics. If you have any doubt about any topic/point please submit it in the discussion section... it will be answered as soon as possible.
    After all of this... when you feel confident about the particular topic/chapter then take the quiz.

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