# How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3 - 2x^2 - x +1#?

Find and test the critical numbers, then find

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To find the exact relative maximum and minimum of the polynomial function ( f(x) = x^3 - 2x^2 - x +1 ), follow these steps:

- Find the critical points by taking the derivative of the function and setting it equal to zero.
- Determine the intervals where the function is increasing or decreasing using the first derivative test.
- Use the second derivative test to classify the critical points as relative maximums, relative minimums, or points of inflection.

Let's find the critical points first:

( f'(x) = 3x^2 - 4x - 1 )

Setting ( f'(x) ) equal to zero and solving for ( x ):

( 3x^2 - 4x - 1 = 0 )

The solutions for ( x ) will give the critical points.

Next, determine the intervals of increase and decrease by analyzing the sign of ( f'(x) ) in these intervals.

Finally, use the second derivative test on the critical points to determine whether they correspond to relative maximums, relative minimums, or points of inflection.

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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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