Worksheet by Kuta Software LLC. Kuta Software - Infinite Calculus ... B S EAjl4lk FruiogGhUt5sf srGeisieZrhvPeZdp.9 r 6M
Kuta Software - Infinite Calculus
Name___________________________________
Assignment
Date________________ Period____
For each problem, find all points of relative minima and maxima. 1) y = x 3 − 5 x 2 + 7 x − 5 y 8 6 4 2 −8
−6
−4
−2
2
4
6
8 x
−2 −4 −6 −8
For each problem, find all points of relative minima and maxima. You may use the provided graph to sketch the function. 2) y = x 3 − 6 x 2 + 9 x + 1 y 8 6 4 2 −8
−6
−4
−2
2
4
6
8 x
−2 −4 −6 −8
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Worksheet by Kuta Software LLC
For each problem, find all points of relative minima and maxima. 3) y = − x 3 − 3 x 2 − 1
5) y = x 4 − x 2
7) y = (2 x − 8)
4) y = x 4 − 2 x 2 + 3
6) y = −
2 3
2 x −4 2
5
2
1 8) y = − ( x − 4) 3 − 2( x − 4) 3 5
Critical thinking questions: 9) Give an example function f ( x) where f '' (0) = 0 and there is no relative minimum or maximum at x = 0.
10) Give an example function f ( x) where f '' (0) = 0 and there is a relative maximum at x = 0.
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Assignment
Date________________ Period____
For each problem, find all points of relative minima and maxima. 1) y = x 3 − 5 x 2 + 7 x − 5 y 8 6 4 2 −8
−6
−4
−2
2
4
6
8 x
−2 −4 −6 −8
(
7 86 ,− 3 27 Relative maximum: (1, −2) Relative minimum:
)
For each problem, find all points of relative minima and maxima. You may use the provided graph to sketch the function. 2) y = x 3 − 6 x 2 + 9 x + 1 y 8 6 4 2 −8
−6
−4
−2
2
4
6
8 x
−2 −4 −6 −8
Relative minimum: (3, 1) Relative maximum: (1, 5)
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Worksheet by Kuta Software LLC
For each problem, find all points of relative minima and maxima. 3) y = − x 3 − 3 x 2 − 1
4) y = x 4 − 2 x 2 + 3
Relative minimum: (−2, −5) Relative maximum: (0, −1)
Relative minima: (−1, 2), (1, 2) Relative maximum: (0, 3)
5) y = x 4 − x 2
6) y = −
(
Relative minima: −
2
,−
2 Relative maximum: (0, 0)
)(
1 , 4
2 2
,−
1 4
)
2 x −4 2
( )
Relative minimum: 0,
1 2
No relative maxima.
7) y = (2 x − 8)
2 3
5
2
1 8) y = − ( x − 4) 3 − 2( x − 4) 3 5
Relative minimum: (4, 0) No relative maxima.
(
3
12 2 Relative minimum: 0, − 5 Relative maximum: (4, 0)
)
Critical thinking questions: 9) Give an example function f ( x) where f '' (0) = 0 and there is no relative minimum or maximum at x = 0. Many answers. Ex: f ( x) = 0, x, x 3 , etc
10) Give an example function f ( x) where f '' (0) = 0 and there is a relative maximum at x = 0. Many answers. Ex: f ( x) = − x 4
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Worksheet by Kuta Software LLC
