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AP Intermediate 2nd Year Continuity, Differentiability & Derivatives — practice questions — page 4

Explore 165 free Continuity, Differentiability & Derivatives questions in AP Intermediate 2nd Year 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 91–120 of 165.

Which property is stronger?Read the answer and worked solution →True or false: combining functionsRead the answer and worked solution →Tap every requirement for continuity at a pointRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Complete the one-way implicationRead the answer and worked solution →Flip and pair: condition with what followsRead the answer and worked solution →Complete the chain rule ideaRead the answer and worked solution →If a function is differentiable at a point, it is also:Read the answer and worked solution →Where continuity can failRead the answer and worked solution →Which rule or theorem?Read the answer and worked solution →Functions written with y not isolated are called:Read the answer and worked solution →Continuity of f at c requires the limit at c to equal:Read the answer and worked solution →Theorem 1 concerns two functions that are both:Read the answer and worked solution →Theorem 3 says differentiability at a point implies:Read the answer and worked solution →Combining continuous functionsRead the answer and worked solution →Order the first derivative testRead the answer and worked solution →Flip and pair: symbol with meaningRead 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 →Rolle's theorem requires that on [a, b], in addition to continuity + differentiability:Read the answer and worked solution →For a particle moving along x(t) = t³ − 3t² + 5, the velocity at t = 2 is:Read the answer and worked solution →At a critical point c where f'(c) = 0, if f''(c) > 0, then c is a:Read the answer and worked solution →To find the dimensions of a rectangle with maximum area + perimeter 20, set up:Read the answer and worked solution →The critical points of f(x) = x³ − 3x + 1 are found by solving f'(x) = 0:Read 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 →Match each sign change to its verdictRead the answer and worked solution →The chain rule for related ratesRead the answer and worked solution →True or false: increasing and decreasingRead the answer and worked solution →Tap every statement true of a local maximum at cRead the answer and worked solution →

Worked practice questions

Which property is stronger?

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Items
  1. Item
    Differentiability
    Category
    Stronger condition
  2. Item
    Implies the other
    Category
    Stronger condition
  3. Item
    Continuity
    Category
    Weaker condition
  4. Item
    Implied by the other
    Category
    Weaker condition
Categories
  1. Item
    Stronger condition
  2. Item
    Weaker condition
Differentiability implies continuity, so it is the stronger condition. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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True or false: combining functions

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Questions
  1. Statement is true
    Yes
    Statement
    The difference of two continuous functions is continuous.
  2. Statement is true
    Yes
    Statement
    The product of two continuous functions is continuous.
  3. Statement is true
    No
    Statement
    A quotient is continuous even where its denominator is zero.
  4. Statement is true
    Yes
    Statement
    The chain rule handles composites of functions.
  5. Statement is true
    Yes
    Statement
    Continuity is defined pointwise, then extended to the domain.
The algebra of continuity, once more. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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Tap every requirement for continuity at a point

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Questions
  1. Items
    1. Text
      The function is defined there
      Matches the category
      Yes
    2. Text
      The limit exists there
      Matches the category
      Yes
    3. Text
      The limit equals the value
      Matches the category
      Yes
    4. Text
      The derivative exists there
      Matches the category
      No
    5. Text
      The function is increasing there
      Matches the category
      No
    Category
    Required for continuity at a point
Three conditions, all needed. Source: syllabus Maths, Ch 5 Continuity and Differentiability.

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