If possible, find the absolute maximum and minimum values of the folowing functi

Question

If possible, find the absolute maximum and minimum values of the folowing function on the set R. f(x y)-3x2-3y 8R (xy)2 +y2 s1) Find the absolute maximum value on the set. Select the correct choice below and, if necessary,fill in the answer boxes within O A· The absolute maximum value is [] and occurs at (Type an ordered pair. Use a comma to separate answers as needed) B. There is no absolute maximum value. Find the absolute minimum value on the set. Select the correct choice below and, i necessary,fillil the answer boxes within your choice. O A· The absolute minimum value is 0 B. There is no absolute minimum value. and occurs at Type an ordered pair. Use a comma to separate answers as needed.)

Explanation / Answer

f=3x² -3y²+8

find partial derivative as

fx= 6x

fy = -6y

find critical point, as

6x =0 gives x =0

-6y= 0 gives y =0

Thus, only critical point, inside the disk is (0,0)

Hence

The absolute maximum value is 11 and occurs at (-1,0),(1,0)

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The absolute minimum value is 5 and occurs at (0,-1),(0,1)

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