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

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In summary, the absolute minimum of the given function y=x Sqr.Root (3-x) in Domain (-infinity, 3) is 0, as the function has a square root and the square root of any number is always positive. The domain of the function is (-infinity, 3), meaning all real numbers less than or equal to 3 can be plugged in for x. To find the absolute minimum of a function, the first derivative is taken and set equal to 0, and the resulting critical points and endpoints of the domain are plugged into the original function to find the smallest y-value. The domain is limited to (-infinity, 3) because square roots cannot have negative numbers under them. Finally, the absolute minimum
  • #1
mattmannmf
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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.
 

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

1. What is the absolute minimum of the given function?

The absolute minimum of y=x Sqr.Root (3-x) in Domain (-infinity, 3) is 0. This is because the function has a square root, and the square root of any number is always positive. Therefore, the minimum value of the function can only be 0.

2. What is the domain of the function?

The domain of the function is (-infinity, 3). This means that all real numbers less than or equal to 3 can be plugged into the function for x.

3. How do you find the absolute minimum of a function?

To find the absolute minimum of a function, you need to take the first derivative of the function and set it equal to 0. Then, solve for x to find the critical points. Next, plug in these critical points and the endpoints of the domain into the original function to find the corresponding y-values. The smallest of these y-values will be the absolute minimum.

4. Why is the domain of the function limited to (-infinity, 3)?

The domain of the function is limited to (-infinity, 3) because the function has a square root. Square roots cannot have negative numbers under them, so the function is undefined for any value of x less than 3. Therefore, the domain is limited to only values greater than or equal to 3.

5. Is the absolute minimum of the function also the global minimum?

Yes, the absolute minimum of the function is also the global minimum. This is because the domain of the function is limited to (-infinity, 3), so the function cannot have a lower value than 0. Therefore, the absolute minimum is also the minimum value of the entire function.

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