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Kuta Software - Infinite Calculus
Name___________________________________
Absolute Extrema
Date________________ Period____
For each problem, find all points of absolute minima and maxima on the given closed interval. 1) y = − x 3 − 6 x 2 − 9 x + 3; [−3, −1]
2) y =
y 8
8 ; [0, 5] x +4 2
y
−8
−6
−4
6
8
4
6
2
4
−2
2
4
6
2
8 x
−2
−8
−6
−4
−2
2
−4
−2
−6
−4
−8
−6
4
6
8 x
−8
3) y = x 3 + 6 x 2 + 9 x + 3; [−4, 0]
x2 5) y = ; [3, 6] 3x − 6
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4) y = x 4 − 3 x 2 + 4; [−1, 1]
2 3
6) y = ( x + 2) ; [−4, −2]
-1-
Worksheet by Kuta Software LLC
For each problem, find all points of absolute minima and maxima on the given interval. 7) y = x 3 − 3 x 2 − 3; (0, 3)
1 3
8) y = (5 x + 25) ; [−2, 2]
y 8
y 8
6
6
4
4
2
2 −8
−6
−4
−2
2
4
6
8 x
−2
−8
−6
−4
−2
2
4
6
8 x
−2
−4
−4
−6
−6
−8
−8
9) y = x 3 − 3 x 2 + 6; [0, ∞)
11) y =
4 ; (−5, −2] 2 x +2
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10) y = x 4 − 2 x 2 − 3; (0, ∞)
7
1
1 14 12) y = − ( x + 1) 3 + ( x + 1) 3 ; (−5, 0) 6 3
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Absolute Extrema
Date________________ Period____
For each problem, find all points of absolute minima and maxima on the given closed interval. 1) y = − x 3 − 6 x 2 − 9 x + 3; [−3, −1]
2) y =
y 8
8 ; [0, 5] x +4 2
y
−8
−6
−4
6
8
4
6
2
4
−2
2
4
6
2
8 x
−2
−8
−6
−4
−2
2
−4
−2
−6
−4
−8
−6
4
6
8 x
−8
Absolute minimum: (−3, 3) Absolute maximum: (−1, 7)
( )
8 29 ( Absolute maximum: 0, 2) Absolute minimum: 5,
3) y = x 3 + 6 x 2 + 9 x + 3; [−4, 0]
4) y = x 4 − 3 x 2 + 4; [−1, 1]
Absolute minima: (−4, −1), (−1, −1) Absolute maxima: (0, 3), (−3, 3)
x2 5) y = ; [3, 6] 3x − 6
Absolute minima: (−1, 2), (1, 2) Absolute maximum: (0, 4)
2 3
6) y = ( x + 2) ; [−4, −2] Absolute minimum: (−2, 0) 3 Absolute maximum: (−4, 4 )
( )
8 Absolute minimum: 4, 3 Absolute maxima: (3, 3), (6, 3)
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-1-
Worksheet by Kuta Software LLC
For each problem, find all points of absolute minima and maxima on the given interval. 7) y = x 3 − 3 x 2 − 3; (0, 3)
1 3
8) y = (5 x + 25) ; [−2, 2]
y 8
y 8
6
6
4
4
2
2 −8
−6
−4
−2
2
4
6
8 x
−2
−8
−6
−4
−2
2
4
6
8 x
−2
−4
−4
−6
−6
−8
−8
Absolute minimum: (2, −7) No absolute maxima.
9) y = x 3 − 3 x 2 + 6; [0, ∞)
3
Absolute minimum: (−2, 15 ) 3 Absolute maximum: (2, 35 )
10) y = x 4 − 2 x 2 − 3; (0, ∞)
Absolute minimum: (2, 2) No absolute maxima.
11) y =
Absolute minimum: (1, −4) No absolute maxima.
7
4 ; (−5, −2] 2 x +2
1
1 14 12) y = − ( x + 1) 3 + ( x + 1) 3 ; (−5, 0) 6 3
No absolute minima.
3
Absolute minimum: (−3, −4 2 ) No absolute maxima.
( )
Absolute maximum: −2,
2 3
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Worksheet by Kuta Software LLC
