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AP Intermediate 2nd Year Continuity, Differentiability & Derivatives — practice questions — page 5

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 121–150 of 165.

Reading the tests backRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →A function f(x) is INCREASING on an interval if for all x in the interval:Read the answer and worked solution →The tangent to y = x² at the point (1, 1) has slope:Read 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 →True or false: scope of this chapterRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →Continuity bingoRead the answer and worked solution →To differentiate an implicit relation you use the:Read the answer and worked solution →A function that fails the limit test at a point is:Read the answer and worked solution →Theorem 2 deals with which kind of function?Read the answer and worked solution →A function whose graph can be drawn without lifting the pen is:Read the answer and worked solution →Does continuity at a point guarantee differentiability?Read the answer and worked solution →If f is not continuous at c, then c is called a point of:Read the answer and worked solution →True or false: continuity and differentiabilityRead the answer and worked solution →Complete the definition of continuityRead the answer and worked solution →The derivative of $\sin(3x)$ is:Read the answer and worked solution →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 →

Worked practice questions

Reading the tests back

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Questions
  1. Question
    f ′ changing negative → positive at c gives
    Choices
    1. local maximum
    2. local minimum
    3. inflexion
    Correct choice
    local minimum
  2. Question
    f ′ keeping its sign through c gives
    Choices
    1. local minimum
    2. local maximum
    3. point of inflexion
    Correct choice
    point of inflexion
  3. Question
    A critical point is where
    Choices
    1. f ′(c) = 0 or f is not differentiable
    2. f(c) = 0
    3. f ″(c) = 0
    Correct choice
    f ′(c) = 0 or f is not differentiable
  4. Question
    The absolute maximum over [a, b] is found by comparing
    Choices
    1. only critical values
    2. critical values and endpoint values
    3. only endpoint values
    Correct choice
    critical values and endpoint values
Straight recall of the two derivative tests. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Spot the odd one

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Questions
  1. Items
    1. Increasing
    2. Decreasing
    3. Constant
    4. Continuous
    Odd item
    Continuous
  2. Items
    1. Absolute maximum
    2. Local maximum
    3. Local minimum
    Odd item
    Absolute maximum
  3. Items
    1. f ′(c) = 0
    2. f(c) < 0
    3. f ″(c) < 0
    Odd item
    f(c) < 0
Grouped by which decision each belongs to. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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Complete the second derivative test

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Missing parts
  1. Answer
    maxima
    Choices
    1. maxima
    2. minima
    3. inflexion
  2. Answer
    minima
    Choices
    1. maxima
    2. minima
    3. inflexion
  3. Answer
    fails
    Choices
    1. fails
    2. still applies
    3. gives inflexion
Complete the statement
If f ′(c) = 0 and f ″(c) < 0 then c is a point of local {0}. If f ′(c) = 0 and f ″(c) > 0 then c is a point of local {1}. If f ″(c) = 0 as well, the test {2}.
Both halves of the test, plus the case where it gives up. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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