Question

Use a graphing utility to graph the function. Choose a window that allows all relative extrema and points of inflection to be identified on the graph. \(y=x \sqrt{x^{2}-9}\)

Short answer

The steps involve entering the function into a graphing utility, choosing an appropriate window to view the entire function, visually identifying any relative extrema, and noting any points where the graph changes concavity (points of inflection). Exact points will depend on the specific graphing utility and window chosen.

Step-by-step solution

Enter Function into the Graphing Utility

Start by entering the function \(y=x \sqrt{x^{2}-9}\) into the graphing utility. Ensure the equation is entered correctly.

Choose an Appropriate Graphing Window

Choose an appropriate graphing window that allows the entirety of the function to be viewed. You might need to experiment with different window sizes to achieve this.

Identify Relative Extrema

Examine the graph for any clear peaks (local maxima) or valleys (local minima). These represent the relative extrema of the function. Don't forget to include the x values associated with these points.

Identify Points of Inflection

Points of inflection are where the graph changes concavity. Look for areas where the graph transitions from curving upward to curving downward (or vice versa). It's crucial to also include the x values associated with these points.