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JEE Advanced Continuity, Differentiability & Derivatives — practice questions — page 4

Explore 112 free Continuity, Differentiability & Derivatives questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity, Differentiability & Derivatives questions and exercises with answers

Showing questions 91–112 of 112.

Spot the one that does not belongRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →True or false: continuity and differentiabilityRead the answer and worked solution →Complete the definition of continuityRead the answer and worked solution →The derivative of $\sin(3x)$ is:Read the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Match each function to its derivative.Read the answer and worked solution →Two true, one falseRead the answer and worked solution →Tap every operation that preserves continuityRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: rule with what it handlesRead the answer and worked solution →The second derivative testRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Which way does the implication run?Read the answer and worked solution →Assertion and reason: continuityRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →

Worked practice questions

Spot the one that does not belong

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Questions
  1. Items
    1. f ′(x) > 0
    2. f ′(x) < 0
    3. f increasing
    Odd item
    f ′(x) < 0
  2. Items
    1. Local maximum
    2. Local minimum
    3. Point of inflexion
    Odd item
    Point of inflexion
  3. Items
    1. Chain rule
    2. First derivative test
    3. Second derivative test
    Odd item
    Chain rule
  4. Items
    1. f ′(c) = 0
    2. f(c) = 0
    3. f not differentiable at c
    Odd item
    f(c) = 0
Each group comes from one summary bullet. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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True or false: scope of this chapter

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Questions
  1. Statement is true
    Yes
    Statement
    This chapter covers increasing and decreasing functions.
  2. Statement is true
    Yes
    Statement
    This chapter gives a working rule for absolute maxima.
  3. Statement is true
    Yes
    Statement
    This chapter defines a critical point.
  4. Statement is true
    No
    Statement
    A point of inflexion is a kind of local maximum.
  5. Statement is true
    Yes
    Statement
    The first derivative test needs f continuous at the critical point.
Keeps the topic honest about what the current edition contains. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Match each situation to the right tool

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Matching pairs
  1. Left
    Two quantities both changing with time
    Right
    chain rule for related rates
  2. Left
    Deciding maximum or minimum at a critical point
    Right
    first or second derivative test
  3. Left
    Largest value over a closed interval
    Right
    the working rule with endpoints
Choosing the tool is most of the marks in this chapter. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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