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Lesson: Locating Absolute Extrema

Absolute extrema are two points, the absolute maximum and minimum, where the function has the largest value at the absolute maximum and the smallest value at the absolute minimum. In this lesson, you will know how to find those two points.

Worksheet: Locating Absolute Extrema • 8 Questions

Q1:

Determine the absolute maximum and minimum values of the function on the interval .

  • AThe absolute maximum is 6, and the absolute minimum is .
  • BThe absolute maximum is 2, and the absolute minimum is .
  • CThe absolute maximum is 128, and the absolute minimum is .
  • DThe absolute maximum is 12, and the absolute minimum is .

Q2:

Determine the absolute maximum and minimum values of the function , in the interval , approximated to two decimal places.

  • Aabsolute maximum = 170.80, absolute minimum = 113.10
  • Babsolute maximum = , absolute minimum =
  • Cabsolute maximum = 2.00, absolute minimum = 2.00
  • Dabsolute maximum = 47.00, absolute minimum = 2.00

Q3:

Determine the absolute maximum and minimum values of the function in the interval .

  • Ahas no local maximum or minimum values
  • BThe absolute maximum value is , and the absolute minimum value is 48.
  • CThe absolute maximum value is , and the absolute minimum value is .
  • DThe absolute maximum value is 32, and the absolute minimum value is 0.
  • EThe absolute maximum value is , and the absolute minimum value is .

Q4:

Find the absolute maximum and minimum values of the function on the interval .

  • AThe absolute maximum is 2, and the absolute minimum is .
  • BThe absolute maximum is 0, and the absolute minimum is .
  • CThe absolute maximum is 0, and the absolute minimum is .
  • DThe absolute maximum is , and the absolute minimum is .

Q5:

Determine the absolute maximum and minimum values of the function on the interval .

  • AThe absolute maximum equals , and the absolute minimum equals .
  • BThe absolute maximum equals , and the absolute minimum equals .
  • CThe absolute maximum equals , and the absolute minimum equals .
  • DThe absolute maximum equals , and the absolute minimum equals .
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