# What are the absolute extrema of #f(x)=(x^2 - 1)^3 in[-oo,oo]#?

To compute critical points of a function, we need to compute the first derivative, and then to find its zeroes.

As a general rule, we have that

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The absolute extrema of ( f(x) = (x^2 - 1)^3 ) on the interval ([- \infty, \infty]) are as follows:

The function has a local minimum at ( x = -1 ) and a local maximum at ( x = 1 ). Since the function approaches infinity as ( x ) approaches infinity or negative infinity, there are no absolute minima. The absolute maximum occurs at ( x = 1 ), where ( f(x) = 0 ).

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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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