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MP DTE Application of Derivatives — practice questions — page 3

Explore 69 free Application of Derivatives questions in MP DTE 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 61–69 of 69.

Flip and pair: symbol with meaningRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →Tap every statement true of a local maximum at cRead the answer and worked solution →Reading the tests backRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →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

Flip and pair: symbol with meaning

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Matching pairs
  1. A
    f ′(x)
    B
    first derivative
  2. A
    f ″(x)
    B
    second derivative
  3. A
    dy/dx
    B
    rate of change of y with x
  4. A
    f ′(c) = 0
    B
    stationary point
  5. A
    c
    B
    a critical point
The chapter's notation. 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
  4. Left
    Whether the graph rises or falls
    Right
    the sign of f ′(x)
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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Tap every statement true of a local maximum at c

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Questions
  1. Items
    1. Text
      f ′ changes from positive to negative at c
      Matches the category
      Yes
    2. Text
      f ′(c) = 0 and f ″(c) < 0
      Matches the category
      Yes
    3. Text
      f ′ changes from negative to positive at c
      Matches the category
      No
    4. Text
      f ′(c) = 0 and f ″(c) > 0
      Matches the category
      No
    5. Text
      f ′ keeps the same sign through c
      Matches the category
      No
    Category
    Indicates a LOCAL MAXIMUM at c
The two tests give two different signatures for the same conclusion. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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