Question
Find the absolute maximum and minimum values of the following function on the given set
What is the absolute maximum value? Select the correct choice below and, if necessary, fill in the answer box to
complete your choice.
A. The absolute maximum value is 49 . (Simplify your answer.)
B. There is no absolute maximum value.
What is the absolute minimum value? Select the correct choice below and, if necessary, fill in the answer box to
complete your choice.
A. The absolute minimum value is . (Simplify your answer.)
B. There is no absolute minimum value.
What is the absolute maximum value? Select the correct choice below and, if necessary, fill in the answer box to
complete your choice.
A. The absolute maximum value is 49 . (Simplify your answer.)
B. There is no absolute maximum value.
What is the absolute minimum value? Select the correct choice below and, if necessary, fill in the answer box to
complete your choice.
A. The absolute minimum value is . (Simplify your answer.)
B. There is no absolute minimum value.
Ask by Griffiths Wade. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The absolute maximum value is 49, and the absolute minimum value is 0.
Solution
We start by rewriting the function:
Complete the square in
Thus, the function can be written as:
This shows that
The region is given by:
which is a disk of radius 5 centered at the origin.
Absolute Minimum:
Since
Check that
Thus, the absolute minimum value is:
Absolute Maximum:
The absolute maximum occurs where the squared distance from
The maximum distance from
The distance between the center of the disk
Thus, the farthest distance from
Therefore, the function reaches its maximum at a point on the boundary such that the distance is
Final Answers:
- The absolute maximum value is 49.
- The absolute minimum value is 0.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the absolute maximum and minimum values of the function
Now the function is expressed as:
Finding the minimum value:
- The term
is non-negative, and it achieves its minimum when and . Thus, the minimum value is:
This point lies inside the region since
Finding the maximum value:
- The maximum will occur on the boundary where
. - To evaluate points on the boundary, we can express
in terms of : or and substitute back into .
By checking some critical points on the circle:
-
: -
: -
: -
:
The maximum value found occurs at
Final answers:
- The absolute maximum value is 49.
- The absolute minimum value is 0.
Thus, select option A for absolute maximum and option A for absolute minimum, filling in the answers accordingly:
The absolute maximum value is 49.
The absolute minimum value is 0.
