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5-98.
  1. Using the graph of f ′(x), determine the values of x where f(x) has a local minimum, local maximum or point of inflection. Justify your answer for each point. Homework Help ✎

You are looking at a graph of f '(x), which shows all the slopes of f(x).

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

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

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

x = −3: local minimum
x = 1: local maximum
x = −1: inflection point