# Worksheet: Absolute Extrema

Q1:

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

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

Q2:

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

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

Q3:

Find the absolute maximum and absolute minimum of

• A The absolute maximum value is 64 at , and the absolute minimum value is 25 at .
• B The absolute maximum value is 25 at , and the absolute minimum value is 4 at .
• C The absolute maximum value is 64 at , and the absolute minimum value is 25 at .
• D The absolute maximum value is 64 at , and the absolute minimum value is 4 at .
• E The function has no absolute maximum or minimum values.

Q4:

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

• A The absolute maximum equals , and the absolute minimum equals .
• B The absolute maximum equals , and the absolute minimum equals .
• C The absolute maximum equals , and the absolute minimum equals .
• D The absolute maximum equals , and the absolute minimum equals .

Q5:

Find the absolute maximum and minimum values rounded to two decimal places of the function , .

• AThe absolute maximum is 0, and the absolute minimum is .
• BThe absolute maximum is 0, and the absolute minimum is 1.84.
• CThe absolute maximum is , and the absolute minimum is 0.
• DThe absolute maximum is 1.84, and the absolute minimum is 0.
• EThe absolute maximum is 1.84, and the absolute minimum is .

Q6:

In the interval , determine the absolute maximum and minimum values of the function and round them to the nearest hundredth.

• AThe absolute maximum is 11.00, and the absolute minimum is 6.00.
• BThe absolute maximum is 11.00, and the absolute minimum is .
• CThe absolute maximum is , and the absolute minimum is .
• DThe absolute maximun is 7.00, and the absolute minimum is .

Q7:

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

• Aabsolute maximum = 9.00, absolute minimum = 1.00
• Babsolute maximum = 68.00, absolute minimum = 1.00
• Cabsolute maximum = 242.00, absolute minimum = 172.20
• Dabsolute maximum = 0.05, absolute minimum =

Q8:

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

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

Q9:

The concentration of a drug in a patientβs bloodstream hours after administration is . After about how many hours would the drugβs concentration be at its highest? If necessary, round your answer to two decimal places.

Q10:

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

• A absolute maximum is , absolute minimum is
• B absolute maximum is , absolute minimum is
• C absolute maximum is , absolute minimum is
• Dabsolute maximum is , absolute minimum is

Q11:

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

• A The absolute maximum value is 32, and the absolute minimum value is 0.
• B The absolute maximum value is , and the absolute minimum value is .
• C The absolute maximum value is , and the absolute minimum value is 48.
• D The absolute maximum value is , and the absolute minimum value is .
• E has no local maximum or minimum values

Q12:

Consider the function whose graph is shown.

Is it true that for all ?

• Ayes
• Bno

Does this mean that 5 is a maximum for the function on the interval ?

• Ano
• Byes

Is on the interval ?

• Ano
• Byes

Is 2 a minimum for the function on the interval ?

• Ano
• Byes

You are told that if , then is continuous on . Why does this example not contradict the extreme value theorem?

• Abecause the function is not a polynomial
• Bbecause the function has a minimum
• Cbecause the domain is bounded
• Dbecause the domain is not a closed interval
• Ebecause on its domain

Q13:

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

• AThe absolute maximum is 52, and the absolute minimum is 0.
• BThe absolute maximum is 52, and the absolute minimum is .
• CThe absolute maximum is 54, and the absolute minimum is 18.
• DThe absolute maximum is 81, and the absolute minimum is .