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Rajasthan Board Class 12 (RBSE) Optimization — practice questions

Explore 26 free Optimization questions in Rajasthan Board Class 12 (RBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Optimization questions and exercises with answers

Showing questions 1–26 of 26.

Fill the calculus turning point ruleRead the answer and worked solution →What does the sign of f ′(x) tell you?Read the answer and worked solution →Complete the definition of a critical pointRead the answer and worked solution →Order the first derivative testRead the answer and worked solution →Match each sign change to its verdictRead the answer and worked solution →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

Fill the calculus turning point rule

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Missing parts
  1. Answer
    increasing
    Choices
    1. increasing
    2. decreasing
    3. constant
  2. Answer
    above
    Choices
    1. below
    2. above
    3. equal to
  3. Answer
    minimum
    Choices
    1. maximum
    2. minimum
    3. constant
Complete the statement
A function is {0} on an interval where the first derivative is positive, and a critical point where the second derivative is {1} zero is a local {2}.
Instructions
Tap the right word for each blank to finish the rule for rising curves and turning points.
_Source: Qallery verified question bank, Class 12 State Board, topic Application of Derivatives_

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What does the sign of f ′(x) tell you?

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Items
  1. Item
    f ′(x) > 0 throughout
    Category
    Increasing
  2. Item
    x₁ < x₂ gives f(x₁) < f(x₂)
    Category
    Increasing
  3. Item
    f ′(x) < 0 throughout
    Category
    Decreasing
  4. Item
    x₁ < x₂ gives f(x₁) > f(x₂)
    Category
    Decreasing
  5. Item
    f(x) = c for all x
    Category
    Constant
  6. Item
    f ′(x) = 0 throughout the interval
    Category
    Constant
Categories
  1. Item
    Increasing
  2. Item
    Decreasing
  3. Item
    Constant
Your syllabus gives f ′(x) ≥ 0 on an interval as the test for increasing and f ′(x) ≤ 0 for decreasing. Everything else in the chapter builds on reading that sign. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Complete the definition of a critical point

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Missing parts
  1. Answer
    0
    Choices
    1. 0
    2. 1
    3. undefined
  2. Answer
    not differentiable
    Choices
    1. not differentiable
    2. not continuous
    3. not defined
Complete the statement
A point c in the domain of f is a critical point if either f ′(c) = {0}, or f is {1} at c.
Your syllabus's definition covers two cases, and the second one is the one people forget. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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