What are the absolute extrema of #f(x) =x/(x^2x+1) in[0,3]#?
Absolute minimum is
Testing the endpoints of the intevral and the critical number in the interval, we find:
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To find the absolute extrema of ( f(x) = \frac{x}{x^2  x + 1} ) on the interval ([0, 3]), you first need to check critical points and endpoints.
 Find critical points by setting the derivative equal to zero and solving for ( x ).
[ f'(x) = \frac{(x^2  x + 1)  x(2x  1)}{(x^2  x + 1)^2} = 0 ]
Solve for ( x ) to find critical points.

Check endpoints of the interval ([0, 3]), which are ( x = 0 ) and ( x = 3 ).

Evaluate ( f(x) ) at critical points and endpoints.

Determine the maximum and minimum values of ( f(x) ) from the values obtained in step 3.
These steps will help identify the absolute extrema of the function ( f(x) ) on the interval ([0, 3]).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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