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Tap every point you must test for an absolute maximum

Exercise and reference answers

Questions
  1. Items
    1. Text
      Points where f ′(x) = 0
      Matches the category
      Yes
    2. Text
      Points where f is not differentiable
      Matches the category
      Yes
    3. Text
      The two endpoints of the interval
      Matches the category
      Yes
    4. Text
      Every point of the interval
      Matches the category
      No
    5. Text
      Points where f(x) = 0
      Matches the category
      No
    Category
    Must be evaluated when hunting an absolute maximum
  2. Items
    1. Text
      f ′ does not change sign there
      Matches the category
      Yes
    2. Text
      It is neither a local maximum nor a local minimum
      Matches the category
      Yes
    3. Text
      It is always the highest point
      Matches the category
      No
    4. Text
      f ′ changes from positive to negative
      Matches the category
      No
    Category
    True of a point of inflexion

Explanation

The endpoints matter as much as the critical points, which is the whole point of the working rule. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
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