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ISC Class 12 Continuity, Differentiability & Derivatives — practice questions — page 2

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 31–60 of 115.

True or False: Derivatives (ISC 12)Read the answer and worked solution →Match the Derivative (ISC 12)Read the answer and worked solution →Fill the calculus turning point ruleRead the answer and worked solution →An alternative to repeated product rule for many factors is:Read the answer and worked solution →True or false about continuityRead the answer and worked solution →Match the calculus ideaRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →The rule for differentiating a composite function is the:Read the answer and worked solution →Order the test for continuity at a pointRead the answer and worked solution →True or false: reading the definitionsRead the answer and worked solution →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 →

Worked practice questions

True or False: Derivatives (ISC 12)

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Questions
  1. Statement is true
    Yes
    Statement
    The derivative of sin x is cos x.
  2. Statement is true
    Yes
    Statement
    The derivative of a constant is zero.
  3. Statement is true
    No
    Statement
    The derivative of e^x is x e^(x-1).
  4. Statement is true
    Yes
    Statement
    The derivative of ln x is 1/x.
  5. Statement is true
    Yes
    Statement
    The derivative of x^n is n x^(n-1).
Instructions
Tap True or False for each statement.

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Match the Derivative (ISC 12)

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Matching pairs
  1. Left
    sin x
    Right
    cos x
  2. Left
    cos x
    Right
    -sin x
  3. Left
    tan x
    Right
    sec^2 x
Instructions
Pair each function with its derivative.

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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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