# How do you graph #f(x)=1/x-3x^3# using the information given by the first derivative?

Look for zeros on the first and second derivatives.

Start by finding the first and second derivative.

Conclusion:

taking information from the second derivative into account:

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To graph ( f(x) = \frac{1}{x} - 3x^3 ) using 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 and negative.
- Use the behavior of the first derivative to determine the increasing and decreasing intervals.
- Analyze the concavity of the function using the second derivative.
- Use the critical points, increasing/decreasing intervals, and concavity to sketch the graph of the function.

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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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