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This section has two different main concepts.
The first is looking at a graph of a derivative and gleaning necessary information off of this graph. The information that can be asked about includes, but is not limited to: critical points, inflections points, relative extrema and concavity.
The second main part of this section is the Mean Value Theorem. To find place where the Mean Value Theorem is guaranteed on an interval, you need to find the average rate of change and determine where the average rate of change matches the instantaneous rate of change on that interval. The Mean Value Theorem guarantees that for a continuous and differentiable function that there is at least one location where the mean value is satisfied in between the end points of the interval.
An example problem:
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