# How do you graph the derivative of a function when you are given the graph of the function?

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To graph the derivative of a function when you are given the graph of the function, follow these steps:

- Identify the critical points of the function on the given graph. These points occur where the function has maximum, minimum, or points of inflection.
- Determine the intervals where the function is increasing or decreasing based on the slope of the original function's graph.
- Use the information from step 2 to determine the sign of the derivative in each interval. If the function is increasing, the derivative is positive; if the function is decreasing, the derivative is negative.
- Identify any points of discontinuity or sharp changes in the graph of the original function. These may indicate points where the derivative is undefined or has a vertical tangent.
- Plot the critical points, intervals of increase and decrease, and any points of discontinuity on the graph of the derivative.
- Sketch the graph of the derivative, ensuring that it reflects the sign changes and behavior of the original function.

By following these steps, you can graph the derivative of a function using the given 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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- How do you find the derivative of #f(x)=9-1/2x# using the limit process?

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