©E 9250i163P WKAu2tWao 0S1oCfItxwka4rbeV 0LvLoC5.Z I AA5lol2 5rpikgfhItbsX trFeyscekrdvNeYdP.6 U XMLacdGeD 7wmiItphy XIangfhivnhiPtRe2 lCsaOlBc2utlMuZsQ.l Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus Name___________________________________

Period____Date________________Rolle's Theorem

For each problem, find the values of

c that satisfy Rolle's Theorem.

1)

y =

x2 + 4

x + 5; [−3, −1]

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

2)

y =

x3 − 2

x2 −

x − 1; [

−1, 2]

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

3)

y =

−

x3 + 2

x2 +

x − 6; [

−1, 2] 4)

y =

x3 − 4

x2 −

x + 7; [

−1, 4]

5)

y =

−

x3 + 2

x2 +

x − 1; [

−1, 2] 6)

y =

x3 −

x2 − 4

x + 3; [

−2, 2]

7)

y =

−

x2 − 2

x + 15

−

x + 4; [

−5, 3] 8)

y =

x2 − 2

x − 15

−

x + 6; [

−3, 5]

-1-

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9)

y =

−

x2 + 2

x + 15

x + 4; [

−3, 5] 10)

y =

x2 +

x − 6

−

x + 3; [

−3, 2]

11)

y =

−2sin

(

2

x); [

−

π,

π] 12)

y =

sin

(

2

x); [

−

π,

π]

For each problem, determine if Rolle's Theorem can be applied. If it can, find all values of

c that satisfy

the theorem. If it cannot, explain why not.

13)

y =

x2 −

x − 12

x + 4; [

−3, 4] 14)

y =

−

x2 − 2

x + 8

−

x + 3; [

−4, 2]

15)

y =

−

x2 + 36

x + 7; [

−6, 6] 16)

y =

−

x2 + 4

4

x; [−2, 2]

17)

y =

2tan

(

x); [

−

π,

π] 18)

y =

−2cos

(

2

x); [

−

π,

π]

-2-

©v a2b0A113A qK1uXtKaT 8SCoEf6tRw9aurSeF JLIL1C4.b h hANlal0 sr8ihgvhKt7sm IrXerswejrnvyehdD.T T tMEaCdeee Uw6i6t3hL vIAnsfNi3ndiNtMe1 KCoa8lJcGuolRuYsK.Z Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus Name___________________________________

Period____Date________________Rolle's Theorem

For each problem, find the values of

c that satisfy Rolle's Theorem.

1)

y =

x2 + 4

x + 5; [−3, −1]

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

{−2}

2)

y =

x3 − 2

x2 −

x − 1; [

−1, 2]

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

{

2 + 7

3,

2 −

7

3 }

3)

y =

−

x3 + 2

x2 +

x − 6; [

−1, 2]

{

2 −

7

3,

2 + 7

3 }

4)

y =

x3 − 4

x2 −

x + 7; [

−1, 4]

{

4 + 19

3,

4 −

19

3 }

5)

y =

−

x3 + 2

x2 +

x − 1; [

−1, 2]

{

2 −

7

3,

2 + 7

3 }

6)

y =

x3 −

x2 − 4

x + 3; [

−2, 2]

{

1 + 13

3,

1 −

13

3 }

7)

y =

−

x2 − 2

x + 15

−

x + 4; [

−5, 3]

{1}

8)

y =

x2 − 2

x − 15

−

x + 6; [

−3, 5]

{3}

-1-

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9)

y =

−

x2 + 2

x + 15

x + 4; [

−3, 5]

{−1}

10)

y =

x2 +

x − 6

−

x + 3; [

−3, 2]

{

3 −

6}

11)

y =

−2sin

(

2

x); [

−

π,

π]

{

−3

π

4,

−

π

4,

π

4,

3

π

4 }

12)

y =

sin

(

2

x); [

−

π,

π]

{

−3

π

4,

−

π

4,

π

4,

3

π

4 }

For each problem, determine if Rolle's Theorem can be applied. If it can, find all values of

c that satisfy

the theorem. If it cannot, explain why not.

13)

y =

x2 −

x − 12

x + 4; [

−3, 4]

{

−4 +

2 2}

14)

y =

−

x2 − 2

x + 8

−

x + 3; [

−4, 2]

{

3 −

7}

15)

y =

−

x2 + 36

x + 7; [

−6, 6]

{

−7 + 13}

16)

y =

−

x2 + 4

4

x; [−2, 2]

The function is not continuous on [−2, 2]

17)

y =

2tan

(

x); [

−

π,

π]

The function is not continuous on [

−

π,

π]

18)

y =

−2cos

(

2

x); [

−

π,

π]

{

−

π

2, 0,

π

2 }

-2-

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