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MAT 150 – Class #20

MAT 150 – Class #20. Topics: Identify Graphs of Higher-Degree P olynomials F unctions Graph Cubic and Q uartic Functions Find Local Extrema and Absolute Extrema Modeling Cubic and Quartic Functions. Higher-Degree Polynomial Functions.

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MAT 150 – Class #20

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  1. MAT 150 – Class #20 • Topics: • Identify Graphs of Higher-Degree Polynomials Functions • Graph Cubic and Quartic Functions • Find Local Extrema and Absolute Extrema • Modeling Cubic and Quartic Functions

  2. Higher-Degree Polynomial Functions • Higher-degree polynomials functions with degree higher than 2. • Examples:

  3. Example of Higher-Degree Polynomial

  4. Two Important Higher-Degree Polynomials • Cubic Function • Quartic Function

  5. Key Features of Higher-Degree Polynomials • In general, the graph of a polynomial function of degree n has at most n x-intercepts. • Local extremaPoints - Turning Points on these graphs • Local minimum point- where the curve changes from decreasing to increasing • Local Maximum point – Where the curve changes from increasing to decreasing • Absolute Maximum Point – the highest point on the graph over an interval • absolute minimum point – The lowest Point on the graph over an interval

  6. Graph • Using the appropriate window, graph . • Find the local maximum and local minimum, if possible. • Where is the absolute maximum of this function on the interval [0, 6]?

  7. Types of Polynomials

  8. Match the Function to the Graph 1 2 5 3 4

  9. Graph Questions Use the given graph to graph to • Estimate the x-intercepts • Turning Points • Positive or negative Coefficient • Cubic or Quartic

  10. Assignment Pg. 424-429 #1-2 #5-8 all #11-16 all #33-34 #41, 44, 46

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