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Worksheet: Locating Absolute Extrema

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 .

Q6:

Find, if any, the local maximum and local minimum values of , together with their type.

  • Aabsolute maximum is , absolute minimum is
  • Babsolute maximum is , absolute minimum is
  • Cabsolute maximum is , absolute minimum is
  • Dabsolute maximum is , absolute minimum is

Q7:

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

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

Q8:

Find the absolute maximum and absolute minimum of

  • AThe function has no absolute maximum or minimum values.
  • BThe absolute maximum value is 64 at , and the absolute minimum value is 25 at .
  • CThe absolute maximum value is 64 at , and the absolute minimum value is 4 at .
  • DThe absolute maximum value is 64 at , and the absolute minimum value is 25 at .
  • EThe absolute maximum value is 25 at , and the absolute minimum value is 4 at .