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