# What is the absolute minimum of #f(x)=xlnx#?

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To find the absolute minimum of ( f(x) = x \ln(x) ):

- Take the derivative of ( f(x) ) using the product rule.
- Set the derivative equal to zero and solve for ( x ) to find critical points.
- Evaluate ( f(x) ) at each critical point and also at the endpoints of the domain of ( f(x) ).
- The lowest value obtained from these evaluations will be the absolute minimum of ( f(x) ).

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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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