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5-98.

Using the graph of below, determine the values of where has a local minimum, local maximum, or point of inflection. Justify your answer for each point.

You are looking at a graph of , which shows all the slopes of .

A local minimum on is located where the slopes of change from negative to positive.

A local maximum on is located where the slopes of change from positive to negative.

An inflection point on is where concavity changes, and concavity is a determined by the slope of the the slopes.

: local minimum
: local maximum
: inflection point