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CA Foundation Basic Differential and Integral Calculus — practice questions — page 3

Explore 65 free Basic Differential and Integral Calculus questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Basic Differential and Integral Calculus questions and exercises with answers

Showing questions 61–65 of 65.

A global extremum of a function is taken overRead the answer and worked solution →If f'(x) > 0 throughout an interval, then f isRead the answer and worked solution →What is d/dx of 5e^x?Read the answer and worked solution →The derivative of ln(x^2 + 1) isRead the answer and worked solution →For a straight line y = ax + b, the derivative dy/dx isRead the answer and worked solution →

Worked practice questions

A global extremum of a function is taken over

  1. a single point
  2. a small neighbourhood
  3. the first quadrant
  4. the entire domain
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Correct answer: D. the entire domain

Global or absolute extrema compare the function across its whole domain, unlike local ones.

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If f'(x) > 0 throughout an interval, then f is

  1. constant
  2. decreasing
  3. increasing
  4. oscillating
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Correct answer: C. increasing

A positive derivative means the function value rises as x increases.

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What is d/dx of 5e^x?

  1. 5x e^x
  2. e^(5x)
  3. e^x
  4. 5e^x
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Correct answer: D. 5e^x

A constant multiple stays in front and e^x is unchanged by differentiation.

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