Understanding Local Extrema with Desmos

This video tutorial demonstrates how to use Desmos to find the local extrema of a cubic function. It guides viewers through graphing the function, adjusting the graph view, and identifying the local maximum and minimum points. The tutorial emphasizes the use of Desmos features to accurately determine the coordinates of these extrema.

What is the function being analyzed in this tutorial?

• f(x) = 2x^3 - 36x^2 + 192x + 8

• f(x) = 4x^3 - 48x^2 + 256x + 12

• f(x) = 3x^3 - 24x^2 + 144x + 5

• f(x) = x^3 - 12x^2 + 48x + 10

What is the first step to graph the function on Desmos?

• Switch to projector mode

• Click on the 'Settings' icon

• Enter the function in the input box

• Adjust the X and Y axes

How can you adjust the view of the graph in Desmos?

• By adjusting the axes manually or using zoom

• By changing the color of the graph

• By changing the graph type

• By adding more functions

What is the purpose of adjusting the graph window?

• To add more data points

• To change the graph color

• To find the local extrema

• To change the function

What are the coordinates of the local minimum found in the tutorial?

• (10, 250)

• (4, 328)

• (8, 264)

• (6, 300)

What are the coordinates of the local maximum found in the tutorial?

• (4, 328)

• (8, 264)

• (6, 300)

• (10, 250)

What feature of Desmos helps in identifying the local extrema?

• The graph color

• The automatic labeling of high and low points

• The function input box

• The grid lines

What is the significance of the x-coordinate in the local extrema?

• It is irrelevant to the extrema

• It represents the function value

• It indicates the location of the extrema

• It shows the slope of the graph

What is the significance of the y-coordinate in the local extrema?

• It is irrelevant to the extrema

• It represents the function value at the extrema

• It indicates the location of the extrema

• It shows the slope of the graph

What is the main takeaway from the tutorial?

• Understanding how to change graph colors

• Understanding the history of Desmos

• Learning to find local extrema using Desmos

• Learning to input multiple functions