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JEE Main Unit 2: Differentiation and Fundamental Derivative Rules — practice questions — page 2

Explore 39 free Unit 2: Differentiation and Fundamental Derivative Rules questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 2: Differentiation and Fundamental Derivative Rules questions and exercises with answers

Showing questions 31–39 of 39.

A tank is draining and a student is asked how fast the depth falls when the volume is changing at a known rate. That is again a problem of:Read the answer and worked solution →Catch the derivative toolsRead the answer and worked solution →Pop the shape wordsRead the answer and worked solution →Run the applications gatesRead the answer and worked solution →Slice the calculus wordsRead the answer and worked solution →Slope or bendRead the answer and worked solution →Sort the applicationsRead the answer and worked solution →Type the numberRead the answer and worked solution →Applications bingoRead the answer and worked solution →

Worked practice questions

A tank is draining and a student is asked how fast the depth falls when the volume is changing at a known rate. That is again a problem of:

  1. Repeated trials
  2. Reduced fractions
  3. Rational roots
  4. Related rates
Show answer and solution

Correct answer: D. Related rates

1. Depth and volume are linked by the tank's geometry. 2. Differentiating that link with respect to time connects the two rates. 3. It is a related rates problem. _Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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Catch the derivative tools

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Items
  1. Matches the category
    Yes
    Item
    Related rates
  2. Matches the category
    Yes
    Item
    Linear approx
  3. Matches the category
    Yes
    Item
    Optimization
  4. Matches the category
    Yes
    Item
    Newton method
  5. Matches the category
    No
    Item
    Sonata
  6. Matches the category
    No
    Item
    Pigment
  7. Matches the category
    No
    Item
    Trellis
  8. Matches the category
    No
    Item
    Lantern
Category
Calculus
Instructions
Catch the tools built on derivatives. Let the rest fall.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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Pop the shape words

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Other terms
  1. Sonata
  2. Pigment
  3. Trellis
  4. Lantern
Matching terms
  1. Concave up
  2. Concave down
  3. Inflection
  4. Extremum
Instructions
Pop the words describing a graph's shape. Leave the rest.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._

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