# How do you determine the absolute extreme values for the function #y=x(sqrt(1-x²))# on its domain?

The absolute minimum is:

and the absolute maximum is:

As a real function:

Evaluate now the first derivative:

We can then conclude that:

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To determine the absolute extreme values for the function ( y = x \sqrt{1 - x^2} ) on its domain, follow these steps:

- Find the critical points by taking the derivative of the function and setting it equal to zero.
- Determine the endpoints of the domain.
- Evaluate the function at the critical points and endpoints.
- The largest and smallest values obtained in step 3 are the absolute maximum and minimum values, respectively, of the function on its domain.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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