Infinite Calculus - Intervals of Increase and Decrease, Extrema - Dr. Kokan

Calculus

Name___________________________________ ID: 1

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Intervals of Increase and Decrease, Extrema

Date________________ Period____

For each problem, find the x-coordinates of all critical points and find the open intervals where the function is increasing and decreasing.

1) y = -2x2 - 12x - 18

2) y = -x2 - 4x + 1

3) y = -2x2 - 4x

4) y = x2 - 1

5) y = -2x2 + 4x

6) y = -x3 + 4x2 - 6

Worksheet by Kuta Software LLC

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7) y = x3 - 4x2 + 5 8) y = -x3 + 12x2 - 45x + 52 9) y = x3 - 4x2 + 3 10) y = x3 - 3x2 - 1

x2 11) y =

4x + 4 1

12) y = x - 1

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3x 13) y =

x - 1 2x 14) y = x + 1

x2 15) y = -

4x - 8 16) y = -2x2 - 4x - 4 17) y = -2x2 - 4x - 1

18) y = sin (x); [-p, p]

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19) y = -2sec (x); [-p, p] 20) y = csc (2x); [-p, p]

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Answers to Intervals of Increase and Decrease, Extrema (ID: 1)

1) Critical point at: x = -3

Increasing: (-?, -3) Decreasing: (-3, ?)

2) Critical point at: x = -2

Increasing: (-?, -2) Decreasing: (-2, ?)

3) Critical point at: x = -1

Increasing: (-?, -1) Decreasing: (-1, ?)

4) Critical point at: x = 0

Increasing: (0, ?) Decreasing: (-?, 0)

5) Critical point at: x = 1

Increasing: (-?, 1) Decreasing: (1, ?)

8 6) Critical points at: x = 0,

3

( ) ( ) 8

Increasing: 0,

Decreasing: (-?, 0),

8 , ?

3

3

8 7) Critical points at: x = 0,

3

8) Critical points at: x = 3, 5

Increasing: (3, 5) Decreasing: (-?, 3), (5, ?)

( ) ( ) Increasing: (-?, 0),

8 , ?

8 Decreasing: 0,

3

3

8 9) Critical points at: x = 0,

3

10) Critical points at: x = 0, 2

Increasing: (-?, 0), (2, ?) Decreasing: (0, 2)

( ) ( ) Increasing: (-?, 0),

8 , ?

8 Decreasing: 0,

3

3

11) Critical points at: x = -2, 0

Increasing: (-?, -2), (0, ?) Decreasing: (-2, -1), (-1, 0)

12) No critical points exist.

Increasing: No intervals exist. Decreasing: (-?, 1), (1, ?)

13) No critical points exist.

Increasing: No intervals exist. Decreasing: (-?, 1), (1, ?)

14) No critical points exist.

Increasing: (-?, -1), (-1, ?) Decreasing: No intervals exist.

15) Critical points at: x = 0, 4

Increasing: (0, 2), (2, 4) Decreasing: (-?, 0), (4, ?)

16) Critical point at: x = -1

Increasing: (-?, -1) Decreasing: (-1, ?)

17) Critical point at: x = -1

Increasing: (-?, -1) Decreasing: (-1, ?)

pp 18) Critical points at: x = - ,

22

( ) ( ) ( ) ( ) p p 3p

3p p p 3p

Increasing: - , , , 2p Decreasing: - , - , ,

22 2

2 2 22

19) Critical points at: x = -p, 0, p

( ) ( ) ( ) ( ) p p

pp

Increasing: -p, - , - , 0 Decreasing: 0, , , p

22

22

3p p p 3p 20) Critical points at: x = - , - , ,

4 44 4

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3p p p p p p p 3p

3p p

p 3p

Increasing: - , - , - , - , , , , Decreasing: -p, - , - , 0 , 0, , , p

4 2 2 4 42 2 4

44

44

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