Learn how to determine the local max and min from a graph

The video uses a roller coaster analogy to explain the concepts of global and local maxima and minima. It discusses how these concepts can be visualized by zooming in and out of different sections of a graph. The video further explores the idea of relative maxima and minima, emphasizing the importance of intervals in determining these values. The explanation includes examples of how to identify these points on a graph and the significance of understanding both global and local perspectives.

What analogy is used to explain the concept of maxima and minima?

• A mountain and a valley

• A roller coaster

• A wave in the ocean

• A flight path

What is the difference between global and local maxima?

• Global maxima are the highest points overall, while local maxima are the highest points in a small section.

• Global maxima are the lowest points overall, while local maxima are the lowest points in a small section.

• Global maxima are the highest points in a small section, while local maxima are the highest points overall.

• Global maxima and local maxima are the same.

How can you identify a local maximum within a given interval?

• By averaging all the values in the interval

• By finding the point with the highest value in the interval

• By comparing the point to values outside the interval

• By finding the point with the lowest value in the interval

What is a relative maximum?

• A point that is higher than all other points in the entire function

• A point that is higher than all other points in a specific interval

• A point that is lower than all other points in a specific interval

• A point that is neither higher nor lower than other points

Why is it important to define an interval when determining relative extrema?

• Because intervals allow comparison of points within a specific range

• Because intervals are not necessary for finding extrema

• Because intervals help in finding the absolute maximum

• Because intervals are only used for global extrema