In: Math
Complete a thorough curve analysis of the function ?(?) = ?4 − 12?3 + 48?2 − 64?.
Follow the Algorithm for Curve Sketching as outlined in Section 4.5 of your textbook. You are expected to clearly demonstrate all aspects of the curve analysis, summarize your results clearly, and draw (by hand) an accurate sketch of the function with all key points labelled on the sketch. Show all algebraic steps to your process clearly. Annotate your work to demonstrate what information is gained from each part of the process. State conclusions clearly.
This task does ask you to demonstrate clearly how the function equation, the first derivative, and the second derivative can all be used to fully understand all important characteristics of the graph.