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ISC Class 12 Continuity, Differentiability & Derivatives — practice questions — page 4

Explore 115 free Continuity, Differentiability & Derivatives questions in ISC Class 12 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity, Differentiability & Derivatives questions and exercises with answers

Showing questions 91–115 of 115.

Assertion and reasonRead the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Match each function to its derivative.Read the answer and worked solution →f(x) = x squared at x = 0 is:Read the answer and worked solution →The function f(x) = |x| at x = 0 is continuous but not:Read the answer and worked solution →Continuity valuesRead the answer and worked solution →Complete the theoremRead the answer and worked solution →Two true, one falseRead the answer and worked solution →Tap every operation that preserves continuityRead the answer and worked solution →The chain rule can be extended to composites of:Read the answer and worked solution →Composites of continuous functions, by Theorem 2, are:Read the answer and worked solution →For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:Read the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: rule with what it handlesRead the answer and worked solution →The second derivative testRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Which way does the implication run?Read the answer and worked solution →Assertion and reason: continuityRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Continuous or not?Read the answer and worked solution →Order the continuity checkRead the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →

Worked practice questions

Assertion and reason

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Questions
  1. Reason
    Every differentiable function is continuous, but not the reverse.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Continuity is a weaker requirement than differentiability.
  2. Reason
    The quotient is undefined where the denominator vanishes.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The quotient rule for continuity carries a condition.
  3. Reason
    Continuity compares the limit with the value at that point.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    Continuity at a point guarantees differentiability there.
The reason must genuinely explain the assertion. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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Complete the rate of change statement

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Missing parts
  1. Answer
    rate of change
    Choices
    1. rate of change
    2. total change
    3. average value
  2. Answer
    at that particular point
    Choices
    1. at that particular point
    2. over the whole domain
    3. on average
Complete the statement
If y = f(x), then dy/dx represents the {0} of y with respect to x, and its value at x = x₀ gives that rate {1}.
The chapter opens with the derivative read as a rate. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Which test is being described?

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Items
  1. Item
    Checks the sign of f ′ either side of c
    Category
    First derivative test
  2. Item
    Can identify a point of inflexion
    Category
    First derivative test
  3. Item
    Needs only f ′ to exist near c
    Category
    First derivative test
  4. Item
    Uses the sign of f ″(c)
    Category
    Second derivative test
  5. Item
    Needs f to be twice differentiable at c
    Category
    Second derivative test
  6. Item
    Fails outright when f ″(c) = 0
    Category
    Second derivative test
Categories
  1. Item
    First derivative test
  2. Item
    Second derivative test
Both tests answer the same question by different evidence. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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