### Home > APCALC > Chapter 5 > Lesson 5.2.4 > Problem5-98

5-98.

Using the graph of $y=f^\prime(x)$ below, determine the values of x where f 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