How do you find the critical numbers for #f(x)= x^3 + x^2 + x# to determine the maximum and minimum?
It doesn't have any.
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To find the critical numbers for ( f(x) = x^3 + x^2 + x ) and determine the maximum and minimum, follow these steps:
 Find the derivative of the function, ( f'(x) ).
 Set ( f'(x) ) equal to zero and solve for ( x ) to find critical points.
 Test the critical points to determine whether they correspond to a maximum or minimum or neither.
Applying these steps:

Find the derivative of ( f(x) ): [ f'(x) = \frac{d}{dx} (x^3 + x^2 + x) ]

Set ( f'(x) ) equal to zero and solve for ( x ): [ f'(x) = 3x^2 + 2x + 1 = 0 ]

Solve the quadratic equation ( 3x^2 + 2x + 1 = 0 ) for ( x ). If there are real solutions, those will be the critical points.

Once you have the critical points, test them using the second derivative test or by analyzing the behavior of the function around those points to determine whether they correspond to a maximum, minimum, or neither.

Identify the maximum and minimum points by analyzing the function values at critical points and at endpoints, if applicable.
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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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