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Relative Minimum Relative Maximum RELATIVE EXTREMA.

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Presentation on theme: "Relative Minimum Relative Maximum RELATIVE EXTREMA."— Presentation transcript:

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5 Relative Minimum

6 Relative Maximum RELATIVE EXTREMA

7 1 Relative Minimum Relative Maximum RELATIVE EXTREMA

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9 1 Relative Extrema

10 2 Relative Extrema

11 1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

12 1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

13 1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

14 1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

15 1 Relative Extrema 2 Relative Extrema Polynomial of degree n Can have as many as n - 1 And No More RELATIVE EXTREMA

16 Polynomial of degree n Can have as many as n - 1 And No More RELATIVE EXTREMA

17 Determine the Maximum Number of Relative Extrema for the Polynomial Functions below.

18 Maximum Number of Relative Extrema 4 Maximum Number of Relative Extrema 3

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20 Fundamental Shapes of Graphs Polynomial Functions

21 Quadratic Cubic QuarticQuintic

22 n is even Both ends of the graph rise QuadraticQuartic

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24 n is even

25 Both ends of the graph fall

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27 n is even a > 0 Both ends of the graph rise n is even a < 0 Both ends of the graph fall

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29 n is odd Right end of the graph rises Left end of the graph falls CubicQuintic

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31 n is odd

32 Right end of the graph falls Left end of the graph rises

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34 n is odd a > 0 Right end of the graph rises Left end of the graph falls n is odd a < 0 Right end of the graph falls Left end of the graph rises

35 Product of Linear (Binomial) Factors

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39 1 Degree Sum 1

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41 1 1 1

42 1 1

43 1 1 3 3

44 1 1 3

45 1 1 3 1 1

46 1 1 3 1 6

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49 f (x)

50 Product of Linear (Binomial) Factors

51 Degree 6

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53 Page 341 7, 9, 11

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