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. \(y=(1-x)^{2 / 3}\)

Short answer

Generate the graph of the function \( y=(1-x)^{2 / 3}\) using a graphing utility, then identify the relative extrema and points of inflection in the graph.

Step-by-step solution

Input the Function into the Graphing Utility

The first step is to input the function into the graphing utility. The function is \( y=(1-x)^{2 / 3}\). Ensure to input it correctly to get the accurate graph.

Generate the Graph

After inputting the function, generate the graph. Observe the shape and key points of the graph. It's important to consider the range which allows viewing of all important aspects of the graph.

Identify the Relative Extrema and Points of Inflection

Once the graph has been generated, identify the relative extrema and points of inflection. The relative extrema are the local minimum or local maximum points. There might be intervals on the graph where the function increases or decreases. The points of inflection are points where the curvature of the graph changes.