Understanding Relative Extrema with Desmos

The video tutorial demonstrates how to determine the relative extrema of a polynomial function using Desmos. It guides viewers through entering the function, adjusting the graph window for optimal viewing, and identifying the high and low points on the graph. The tutorial also explains how to record the ordered pairs for these extrema points, emphasizing the importance of understanding the x and y values in this context.

What is the first step in using Desmos to find relative extrema?

• Start graphing

• Enter the polynomial function

• Adjust the graph window

• Click on the intercepts

Which key combination is used to enter an exponent in Desmos?

• Ctrl + 6

• Shift + 6

• Alt + 6

• Cmd + 6

Why is it necessary to adjust the graph window after entering the function?

• To change the color of the graph

• To see the high and low points clearly

• To add more functions

• To zoom in on the x-axis

What is the purpose of changing the Y maximum to 250?

• To view the entire graph

• To see higher points on the graph

• To focus on the x-axis

• To change the graph's color

How can you find the ordered pairs for the extrema points?

• By changing the graph's color

• By clicking on the graph and selecting the points

• By entering them manually

• By adjusting the x-axis

What does the ordered pair (3, 197) represent in the context of the graph?

• A relative minimum

• A relative maximum

• An intercept

• A point of inflection

What is the significance of the x-value in the ordered pair of an extrema?

• It represents the function value

• It is the location of the extrema

• It is the y-intercept

• It is the slope of the tangent

What does the y-value in the ordered pair of an extrema indicate?

• The slope of the tangent

• The location of the extrema

• The local maximum or minimum value

• The x-intercept

What is the local minimum value of the function according to the video?

• 197

• 72

• 3

• 8

At which x-value does the function have a local maximum?

• 197

• 72

• 8

• 3