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04 - Absolute Extrema

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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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-2-
Worksheet by Kuta Software LLC