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UP Board Class 12 Application of Derivatives — practice questions — page 2

Explore 33 free Application of Derivatives questions in UP Board Class 12 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Application of Derivatives questions and exercises with answers

Showing questions 31–33 of 33.

Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →

Worked practice questions

Spot the odd one

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Questions
  1. Items
    1. Increasing
    2. Decreasing
    3. Constant
    4. Continuous
    Odd item
    Continuous
  2. Items
    1. Absolute maximum
    2. Local maximum
    3. Local minimum
    Odd item
    Absolute maximum
  3. Items
    1. f ′(c) = 0
    2. f(c) < 0
    3. f ″(c) < 0
    Odd item
    f(c) < 0
Grouped by which decision each belongs to. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Complete the second derivative test

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Missing parts
  1. Answer
    maxima
    Choices
    1. maxima
    2. minima
    3. inflexion
  2. Answer
    minima
    Choices
    1. maxima
    2. minima
    3. inflexion
  3. Answer
    fails
    Choices
    1. fails
    2. still applies
    3. gives inflexion
Complete the statement
If f ′(c) = 0 and f ″(c) < 0 then c is a point of local {0}. If f ′(c) = 0 and f ″(c) > 0 then c is a point of local {1}. If f ″(c) = 0 as well, the test {2}.
Both halves of the test, plus the case where it gives up. 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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