Relative Minimum

Relative Maximum RELATIVE EXTREMA

1 Relative Minimum Relative Maximum RELATIVE EXTREMA

1 Relative Extrema

2 Relative Extrema

1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

1 Relative Extrema 2 Relative Extrema RELATIVE EXTREMA

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

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

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

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

Fundamental Shapes of Graphs Polynomial Functions

Quadratic Cubic QuarticQuintic

n is even Both ends of the graph rise QuadraticQuartic

n is even

Both ends of the graph fall

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

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

n is odd

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

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

Product of Linear (Binomial) Factors

1 Degree Sum 1

1

1 1 1

1 1

1 1 3

f (x)

Product of Linear (Binomial) Factors

Degree 6

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