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Local and Global Extrema - Expii

Task 4. Use the following graph to explain the local extrema of the function at the given points. Explain clearly how they differ from maximum and minimum values of function. Determine the intervals of all extrema shown in the graph (mention the intervals with the names Ex: (A, B) and specify whether they are increasing or decreasing).

Discuss a DiscoveR: Possible Number of Local Extrema Is it possible for a third-degree polynomial to have extrema one local extremum? Can a fourth-degree polynomial have exactly two local extrema? How many local extrema can polynomials of third, fourth, fifth, and sixth degree have? (Think about the end behavior of such polynomials.) Now give an example of a polynomial that has six local extrema. | Numerade