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Lesson: Locating Absolute Extrema

In this lesson, we will learn how to find the absolute maximum and minimum.

Worksheet • 13 Questions

Q1:

Find, if they exist, the values of the absolute maximum and/or minimum points for the function where .

  • AThe function has an absolute minimum value of and an absolute maximum value of .
  • BThe function has an absolute maximum value of .
  • CThe function has an absolute maximum value of and an absolute minimum value of .
  • DThe function has an absolute minimum value of .
  • EThe function has no absolute maximum or minimum points.

Q2:

If a continuous function on an interval is bounded below but does not achieve a minimum, what can we conclude?

  • AThe interval is not closed.
  • BThe interval is not closed and it is not bounded.
  • CThe interval is not bounded.
  • DThe interval is the entire number line.
  • EEither the interval is not closed or it is not bounded.

Q3:

Find the absolute maximum and absolute minimum of

  • A The absolute maximum value is 64 at π‘₯ = βˆ’ 1 , and the absolute minimum value is 4 at π‘₯ = 5 .
  • B The function has no absolute maximum or minimum values.
  • C The absolute maximum value is 25 at π‘₯ = βˆ’ 3 , and the absolute minimum value is 4 at π‘₯ = 5 .
  • D The absolute maximum value is 64 at π‘₯ = βˆ’ 3 , and the absolute minimum value is 25 at π‘₯ = βˆ’ 1 .
  • E The absolute maximum value is 64 at π‘₯ = βˆ’ 1 , and the absolute minimum value is 25 at π‘₯ = βˆ’ 3 .
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