Understanding Relative Extrema with TI-84

The video tutorial guides viewers through determining the relative extrema of a polynomial function using a TI-84 calculator. It begins with entering the function, graphing it, and adjusting the viewing window for better visibility. The tutorial then demonstrates using the table feature to identify intervals of increase and decrease, leading to the identification of local maxima and minima. The video provides step-by-step instructions for adjusting the axes and using the calculator's calculation menu to find these extrema points.

What is the first step in determining the relative extrema of a polynomial function using the TI-84?

• Graph the function using a standard window.

• Use the table feature to analyze values.

• Adjust the viewing window.

• Enter the function into the calculator.

Why is the standard window not suitable for viewing the polynomial function initially?

• It is too zoomed in.

• It only shows the x-axis.

• It does not display the high and low points.

• It shows too much detail.

What feature of the TI-84 is used to help adjust the viewing window?

• The graph feature.

• The trace feature.

• The zoom feature.

• The table feature.

In which interval does the function change from increasing to decreasing?

• x = 2 to x = 4

• x = 4 to x = 6

• x = 6 to x = 8

• x = 7 to x = 9

What is the purpose of adjusting the x-axis and y-axis settings?

• To make the graph look symmetrical.

• To zoom in on the origin.

• To focus on negative values.

• To include all x and y values of interest.

What is the local minimum value of the function?

• 33

• 144

• 72

• 197

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

• x = 3

• x = 4

• x = 8

• x = 9

What is the local maximum value of the function?

• 197

• 144

• 33

• 72

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

• x = 8

• x = 9

• x = 4

• x = 3

What does the y-value represent in the context of local extrema?

• The function value at the extrema.

• The slope of the function.

• The x-coordinate of the extrema.

• The midpoint of the function.