# Lesson Worksheet: Absolute Extrema Mathematics • 12th Grade

In this worksheet, we will practice finding the absolute maximum and minimum values of a function over a given interval using derivatives.

Q1:

True or False: The extreme value theorem states that only continuous functions on closed bounded intervals have maxima and minima.

• ATrue
• BFalse

Q2:

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

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

Q3:

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

• AThe function has no absolute maximum or minimum points.
• BThe function has an absolute maximum value of 5.
• CThe function has an absolute maximum value of 2 and an absolute minimum value of 5.
• DThe function has an absolute minimum value of 2.
• EThe function has an absolute minimum value of 2 and an absolute maximum value of 5.

Q4:

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

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

Q5:

Find the maximum value of the function .

Q6:

True or False: The function has an absolute minimum over the interval that is equal to .

• ATrue
• BFalse

Q7:

True or False: The function has an absolute maximum over the interval equal to 1.

• AFalse
• BTrue

Q8:

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 .

Q9:

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

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

Q10:

Find the absolute maximum of the function between and .

• A
• B
• C
• D
• E

This lesson includes 40 additional questions and 278 additional question variations for subscribers.