# How do you graph #f(x)=x^3-3x^2-9x+6# using the information given by the first derivative?

graph{x^3-3x^2-9x+6 [-43.74, 46.25, -24.88, 20.13]}

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To graph ( f(x) = x^3 - 3x^2 - 9x + 6 ) using the information from the first derivative, follow these steps:

- Find the critical points by setting the first derivative equal to zero and solving for ( x ).
- Determine the intervals where the first derivative is positive or negative to identify increasing and decreasing sections.
- Locate any local maxima or minima by analyzing the behavior of the first derivative around the critical points.
- Use the behavior of the first derivative to sketch the graph of the function.

To summarize:

- Find critical points by solving ( f'(x) = 0 ).
- Determine intervals of increase and decrease by analyzing the sign of ( f'(x) ).
- Determine local extrema by analyzing the behavior of ( f'(x) ) around critical points.
- Sketch the graph using this information.

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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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