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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Worksheet by Kuta Software LLC
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]
Worksheet by Kuta Software LLC
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19) y = -2sec (x); [-p, p] 20) y = csc (2x); [-p, p]
Worksheet by Kuta Software LLC
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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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Worksheet by Kuta Software LLC
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