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COMEDK Optimization — practice questions

Explore 25 free Optimization questions in COMEDK 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 1–25 of 25.

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

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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Order the first derivative test

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Steps
  1. Find the critical points where f ′(x) = 0 or f is not differentiable
  2. Check f is continuous at the critical point c
  3. Look at the sign of f ′(x) just to the left of c
  4. Look at the sign of f ′(x) just to the right of c
  5. Read the verdict from whether that sign changed, and how
The test is a sign check either side of the critical point, which is why the order matters. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.

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