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BITSAT Application of Derivatives — practice questions — page 2

Explore 51 free Application of Derivatives questions in BITSAT 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 31–51 of 51.

The second derivative testRead the answer and worked solution →True or false: maxima and minimaRead the answer and worked solution →Order the working rule for absolute maxima and minimaRead the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →The chain rule for related ratesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: increasing and decreasingRead the answer and worked solution →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

The second derivative test

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Questions
  1. Question
    f ′(c) = 0 and f ″(c) < 0 means
    Choices
    1. local maximum
    2. local minimum
    3. inflexion
    Correct choice
    local maximum
  2. Question
    f ′(c) = 0 and f ″(c) > 0 means
    Choices
    1. local maximum
    2. local minimum
    3. no conclusion
    Correct choice
    local minimum
  3. Question
    f ′(c) = 0 and f ″(c) = 0 means
    Choices
    1. local maximum
    2. local minimum
    3. the test fails
    Correct choice
    the test fails
  4. Question
    When the second derivative test fails you should
    Choices
    1. go back to the first derivative test
    2. declare no extremum
    3. differentiate a third time
    Correct choice
    go back to the first derivative test
Faster than the first derivative test when it works, and syllabus is explicit that it can fail. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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True or false: maxima and minima

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Questions
  1. Statement is true
    No
    Statement
    Every critical point is a point of local maximum or minimum.
  2. Statement is true
    Yes
    Statement
    If f ′ does not change sign at c, then c is a point of inflexion.
  3. Statement is true
    Yes
    Statement
    The second derivative test needs f to be twice differentiable at c.
  4. Statement is true
    No
    Statement
    f ″(c) = 0 with f ′(c) = 0 settles the question immediately.
  5. Statement is true
    Yes
    Statement
    A point where f is not differentiable can still be a critical point.
Each line is a summary bullet, stated straight or bent. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Order the working rule for absolute maxima and minima

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Steps
  1. Find every critical point of f inside the interval
  2. Take the two endpoints of the interval as well
  3. Evaluate f at all of those points
  4. The largest value found is the absolute maximum
  5. The smallest value found is the absolute minimum
Your syllabus gives this as a four-step rule, and the step people skip is taking the endpoints. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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