AssignmentFor each problem, find all points of relative minima and maxima.1)

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Kuta Software - Infinite Calculus Name___________________________________

Period____

Date________________

Assignment

For each problem, find all points of relative minima and maxima.

1) y = x³ − 5x² + 7x − 5

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 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 = x³ − 6x² + 9x + 1

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

-1-

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For each problem, find all points of relative minima and maxima.

3) y = −x³ − 3x² − 1 4) y = x⁴ − 2x² + 3

5) y = x⁴ − x²

6) y = − 2 x² − 4

7) y =

(

2x − 8

)

2

3 8) y =

−1 5

(

x − 4

)

5

3 − 2

(

x − 4

)

2 3

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.

-2-

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Kuta Software - Infinite Calculus Name___________________________________

Period____

Date________________

Assignment

For each problem, find all points of relative minima and maxima.

1) y = x³ − 5x² + 7x − 5

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Relative minimum:

(

^{73, −8627}

)

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 = x³ − 6x² + 9x + 1

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Relative minimum:

(

3, 1

)

Relative maximum:

(

1, 5

)

-1-

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For each problem, find all points of relative minima and maxima.

3) y = −x³ − 3x² − 1

Relative minimum:

(

−2, −5

)

Relative maximum:

(

0, −1

)

4) y = x⁴ − 2x² + 3

Relative minima:

(

−1, 2

)

,

(

1, 2

)

Relative maximum:

(

0, 3

)

5) y = x⁴ − x²

Relative minima:

(

^{− 22, −14}

)

^,

(

^{22, −14}

)

Relative maximum:

(

0, 0

)

6) y = − 2 x² − 4

Relative minimum:

(

^{0, 12}

)

No relative maxima.

7) y =

(

2x − 8

)

2 3

Relative minimum:

(

4, 0

)

No relative maxima.

8) y =

−1 5

(

x − 4

)

5

3 − 2

(

x − 4

)

2 3

Relative minimum:

(

^{0, −1253 2}

)

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,

x³, 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

)

= −

x⁴

-2-

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