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

Q1:

Determine the absolute maximum and minimum values of the function π¦ = β 2 π₯ 3 on the interval [ β 1 , 2 ] .

Q2:

Determine the absolute maximum and minimum values of the function π¦ = 2 π₯ + π₯ β 3 π₯ β 2 3 2 , in the interval [ β 1 , 1 ] , approximated to two decimal places.

Q3:

Find the absolute maximum and minimum values of the function π¦ = π₯ 4 + 1 π₯ β 4 on the interval [ 1 , 3 ] .

Q4:

Determine the absolute maximum and minimum values of the function π ( π₯ ) = 2 π₯ β 8 π₯ β 1 3 4 2 in the interval [ β 1 , 2 ] .

Q5:

Determine the absolute maximum and minimum values of the function π¦ = π₯ 2 π₯ + 8 on the interval [ 2 , 6 ] .

Q6:

Find, if any, the local maximum and local minimum values of π ( π₯ ) = 5 π₯ 1 3 ( π₯ + 1 ) 2 , together with their type.

Q7:

Find, if they exist, the values of the absolute maximum and/or minimum points for the function π ( π₯ ) = β 3 π₯ + 1 0 where π₯ β [ β 2 , 5 ] .

Q8:

Find the absolute maximum and absolute minimum of

Q9:

In the interval [ β 1 , 2 ] , determine the absolute maximum and minimum values of the function and round them to the nearest hundredth.

Q10:

Determine the absolute maximum and minimum values of the function in the interval [ 1 , 6 ] .

Q11:

The concentration πΆ of a drug in a patientβs bloodstream π‘ hours after administration is πΆ ( π‘ ) = 1 0 0 π‘ 2 π‘ + 7 5 2 . After about how many hours would the drugβs concentration be at its highest? If necessary, round your answer to two decimal places.

Q12:

Find the absolute maximum and minimum values rounded to two decimal places of the function π ( π₯ ) = 5 π₯ π β π₯ , π₯ β [ 0 , 4 ] .

Q13:

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

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