Absolute Min of y=x Sqr.Root (3-x) in Domain (-infinity, 3]

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SUMMARY

The function under discussion is y = x √(3 - x) with a domain of (-∞, 3]. The critical numbers identified are x = 2 and x = 3. The absolute maximum occurs at x = 2, while the absolute minimum does not exist due to the function approaching negative infinity as x approaches negative infinity, contradicting the definition of an absolute minimum value.

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fuction is y=x sqr.root (3-x)

Domain (-infinity, 3]
i got my critical numbers to be x= 2, 3

Now i know the absolute max is x=2.

but for the absolute min, would it be at x=3? or none since the function continues to go to negative infinity as x approaches negative infinity?
 
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Well, assuming that the function goes to negative infinity, then there is no lower bound. It contradicts the definition of an absolute minimum value.
 

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