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Notes 4.1

absolute max/min

local max/min

1 1 2 3 4 5

THEOREM:

Extreme Value Theorem - ____________________________________________________________________

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7/30/2019 NOTES - 4.1 - Extrema

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EX 1:

1 1 2 3 4 5

1 1 2 3 4 5

1 1 2 3 4 5

EX 2:

1 1 2 3 4 5

1 1 2 3 4 5

THEOREM:

Fermats Theorem - _________________________________________________________________________

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_

**NOTE:

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EX 3:

5 4 3 2 1 1 2 3 4 5

5

4

3

2

1

1

2

3

4

5

5 4 3 2 1 1 2 3 4 5

5

4

3

2

1

1

2

3

4

5

critical number - ______________________________________________________________________

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FINDING THE ABSOLUTE MAX/MIN IN A CLOSED INTERVAL

1. ___________________________________________________________________________________\

2. __________________________________________________________________________________

3. ___________________________________________________________________________________

EX 4: Find the absolute max/min values of the function f(x) = x3 3x2 + 1 -1/2 < x < 4

7/30/2019 NOTES - 4.1 - Extrema

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HW: p. 229 # 1 8 all, 11, 45 55 odd

94 A

89 A

79 A69 B

63 C

62 C

60 C

60 C

59 C

57 D

54 D

54 D

51 D

47 E35 E

25 E

24 E

21 E

4 E