04 - Relative Extrema - Kuta Software

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Kuta Software - Infinite Calculus
Name___________________________________
Assignment
For each problem, find all points of relative minima and maxima.
1) y = x 3 − 5x 2 + 7x − 5
Date________________ Period____
8
y
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
x
−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 − 6x 2 + 9x + 1
8
y
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−6
−8

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For each problem, find all points of relative minima and maxima.
3) y = −x 3 − 3x 2 − 1 4) y = x 4 − 2x 2 + 3
5) y = x 4 − x 2 2
6) y = −
x 2 − 4
2
3
7) y = (2x − 8)
8) y = − 1 5
2
5 (x − 4) 3 3
− 2(x − 4)
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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Kuta Software - Infinite Calculus
Name___________________________________
Assignment
For each problem, find all points of relative minima and maxima.
1) y = x 3 − 5x 2 + 7x − 5
Date________________ Period____
8
y
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−6
−8
Relative minimum:
( 7 3 , − 86
27)
Relative maximum: (1, −2)
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 − 6x 2 + 9x + 1
8
y
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−6
−8
Relative minimum: (3, 1)
Relative maximum: (1, 5)

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For each problem, find all points of relative minima and maxima.
3) y = −x 3 − 3x 2 − 1
Relative minimum: (−2, −5)
Relative maximum: (0, −1)
4) y = x 4 − 2x 2 + 3
Relative minima: (−1, 2), (1, 2)
Relative maximum: (0, 3)
5) y = x 4 − x 2
Relative minima: ( − 2
Relative maximum: (0, 0)
2 , − 1 4) , (
2
2 , − 1 4)
2
6) y = −
x 2 − 4
Relative minimum:
( 0, 1 2)
No relative maxima.
2
3
7) y = (2x − 8)
Relative minimum: (4, 0)
No relative maxima.
8) y = − 1 5
2
5 (x − 4) 3 3
− 2(x − 4)
Relative minimum: ( 0, − 12 3 2
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 -2-
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