Master how to identify the absolute/relative local maximum and minimum points of a graph

The video tutorial explains how to identify absolute and local maxima and minima on a graph. It covers the concepts of absolute maximum and minimum, which are the highest and lowest points a graph can reach, respectively. The tutorial also discusses local maxima and minima, which are the highest or lowest points within a specific range. The video uses examples to illustrate these concepts, including graphs with indefinite behavior and piecewise functions. It concludes with a summary of how to determine these points on a graph.

What is the difference between an absolute maximum and a local maximum on a graph?

• A local maximum is the lowest point on the graph, while an absolute maximum is the lowest point within a specific range.

• An absolute maximum is the lowest point on the graph, while a local maximum is the lowest point within a specific range.

• A local maximum is the highest point on the graph, while an absolute maximum is the highest point within a specific range.

• An absolute maximum is the highest point on the graph, while a local maximum is the highest point within a specific range.

If a graph extends indefinitely upwards, what can be said about its absolute maximum?

• The graph has both an absolute and local maximum.

• The graph does not have an absolute maximum.

• The graph has an absolute maximum.

• The graph has a local maximum.

How can you identify a local minimum on a graph?

• It is the highest point within a specific interval.

• It is the highest point on the entire graph.

• It is the lowest point within a specific interval.

• It is the lowest point on the entire graph.

What is a characteristic of piecewise functions in terms of maxima and minima?

• They can have multiple local maxima and minima within different ranges.

• They have no maximum or minimum values.

• They have only one maximum and one minimum value.

• They always have an absolute maximum and minimum.

Can a graph have multiple local maxima with the same height?

• Yes, but only if the graph is a piecewise function.

• No, local maxima must have different heights.

• Yes, a graph can have multiple local maxima with the same height.

• No, a graph can only have one local maximum.