Absolute ExtremaFor each problem, find all points of absolute minima and maxima on the given closed interval.1)

©a 62C0z1b3e DKGuStwaS rS9odf6tVwVaHrVef 7LBLhCU.q l IADlYl9 rrBixg2hxtmsa 7rUeJsHegr3vXeZd5.8 Q hMva8dRe4 hwbiCtyhP NI3nnf0iUnYiXtCeI tCfaEl5csublkutsH.S Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus Name___________________________________

Period____

Date________________

Absolute Extrema

For each problem, find all points of absolute minima and maxima on the given closed interval.

1) y = −x³ − 6x² − 9x + 3; [−3, −1]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

2) y = 8

x² + 4; [0, 5]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

3) y = x³ + 6x² + 9x + 3; [−4, 0] 4) y = x⁴ − 3x² + 4; [−1, 1]

5) y =

x²

3x − 6

; [3, 6] 6) y =

(

x + 2

)

2

3; [−4, −2]

-1-

©E P2z051g3y 0KguFtBag mS4oCfHtEwIasrQew xLMLHCy.T E zAPlMlw FrsiHgVhPtms6 YrvemsTeNrdvuekdv.O 9 PMqaOdCeo FwpiNt1hF zIln6fSiQniiFtleA hC1aulIcYuelBu2se.N Worksheet by Kuta Software LLC

For each problem, find all points of absolute minima and maxima on the given interval.

7) y = x³ − 3x² − 3; (0, 3)

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

8) y =

(

5x + 25

)

1

3; [−2, 2]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

9) y = x³ − 3x² + 6; [0, ∞) 10) y = x⁴ − 2x² − 3; (0, ∞)

11) y = 4

x² + 2; (−5, −2] 12) y =

−1 6

(

)

7 3 +

14 3

(

)

1

3; (−5, 0)

-2-

©y F2G0B1g3K jKAuDtpay SSeoGfGtaw5aMrpe4 3LzLLCV.0 W JA4lXl8 DrviIg3httUsW grleusfe3rSvVeydT.r e uM2ahd8e4 iwVi6tjh6 AIWnOfCiUnUihtNee MC3aKlGcQuXlgufsN.W Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus Name___________________________________

Period____

Date________________

Absolute Extrema

For each problem, find all points of absolute minima and maxima on the given closed interval.

1) y = −x³ − 6x² − 9x + 3; [−3, −1]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Absolute minimum:

(

)

Absolute maximum:

(

)

2) y = 8

x² + 4; [0, 5]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Absolute minimum:

(

)

Absolute maximum:

(

)

3) y = x³ + 6x² + 9x + 3; [−4, 0]

Absolute minima:

(

)

(

)

Absolute maxima:

(

)

(

)

4) y = x⁴ − 3x² + 4; [−1, 1]

Absolute minima:

(

)

(

)

Absolute maximum:

(

)

5) y =

x²

3x − 6

; [3, 6]

Absolute minimum:

(

)

Absolute maxima:

(

)

(

)

6) y =

(

x + 2

)

2

3; [−4, −2]

Absolute minimum:

(

)

Absolute maximum:

(

)

-1-

©t W2r0j1G3l GK2u3t5ae WS1ozfzthwTa0rTej cL9LQCL.m Z fAZlSlD IrLiXgehPtwsh srbeDsPeJrUvReEd5.J 0 DMvaCdfeB MwqiMtvh9 LIqnkfti6nqiEt2eN uCWaYlLc8uYlCu4sK.Q Worksheet by Kuta Software LLC

For each problem, find all points of absolute minima and maxima on the given interval.

7) y = x³ − 3x² − 3; (0, 3)

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Absolute minimum:

(

)

No absolute maxima.

8) y =

(

5x + 25

)

1

3; [−2, 2]

x y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2 2 4 6 8

Absolute minimum:

(

)

Absolute maximum:

(

)

9) y = x³ − 3x² + 6; [0, ∞) Absolute minimum:

(

)

No absolute maxima.

10) y = x⁴ − 2x² − 3; (0, ∞) Absolute minimum:

(

)

No absolute maxima.

11) y = 4

x² + 2; (−5, −2]

No absolute minima.

Absolute maximum:

(

)

12) y =

−1 6

(

)

7 3 +

14 3

(

)

1

3; (−5, 0)

Absolute minimum:

(

)

No absolute maxima.

-2-

Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com