Question
A graph of the function is provided below.

Select each of the true statements from the following:
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All of the above statements are false.
Solution
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True. The derivative of is positive when , that is when the graph of is increasing. The derivative of is negative when , that is when the graph of is decreasing. The derivative of is zero when , that is when the graph of changes from increasing to decreasing or from increasing to decreasing. The derivative of is also zero when the graph of is constant (i.e., a line with zero slope.)
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True. The derivative of is zero when , that is when the graph of changes from increasing to decreasing or from increasing to decreasing.
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True. , since the point is on the graph of
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False.