Interpreting the derivative The graph of f' on the interval [-3,2] is shown in the figure. <IMAGE>


f. Sketch one possible graph of f.

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1. Analyze the graph of the derivative f' to determine where it is positive, negative, and zero. This will help identify the intervals where the function f is increasing or decreasing.
2. Identify the critical points where f' changes sign (from positive to negative or vice versa) and where f' equals zero. These points correspond to local maxima, minima, or points of inflection in the graph of f.
3. Use the information about the intervals of increase and decrease to sketch the general shape of the graph of f. For example, where f' is positive, f should be increasing, and where f' is negative, f should be decreasing.
4. Consider the behavior of f at the endpoints of the interval [-3, 2]. If the graph of f' indicates any specific values at these points, use them to inform the starting and ending points of your sketch.
5. Finally, combine all the information gathered to create a smooth curve that reflects the behavior of f based on the analysis of f'. Ensure that the graph is continuous and follows the trends indicated by the derivative.