For each problem, determine if Rolle's Theorem can be applied. If it can, find all values of c that satisfy the theorem.
Kuta Software - Infinite Calculus
Name___________________________________
Rolle's Theorem
Date________________ Period____
For each problem, find the values of c that satisfy Rolle's Theorem. 1) y = x 2 + 4 x + 5; [−3, −1]
2) y = x 3 − 2 x 2 − x − 1; [−1, 2]
y
−8
−6
−4
y
8
8
6
6
4
4
2
2
−2
2
4
6
8 x
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
4
6
8 x
3) y = − x 3 + 2 x 2 + x − 6; [−1, 2]
4) y = x 3 − 4 x 2 − x + 7; [−1, 4]
5) y = − x 3 + 2 x 2 + x − 1; [−1, 2]
6) y = x 3 − x 2 − 4 x + 3; [−2, 2]
7) y =
− x 2 − 2 x + 15 ; [−5, 3] −x + 4
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8) y =
-1-
x 2 − 2 x − 15 ; [−3, 5] −x + 6
Worksheet by Kuta Software LLC
− x 2 + 2 x + 15 9) y = ; [−3, 5] x+4
x2 + x − 6 10) y = ; [−3, 2] −x + 3
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 =
x 2 − x − 12 ; [−3, 4] x+4
14) y =
−x2 − 2x + 8 ; [−4, 2] −x + 3
− x 2 + 36 15) y = ; [−6, 6] x+7
−x2 + 4 16) y = ; [−2, 2] 4x
17) y = 2tan ( x); [−π, π]
18) y = −2cos (2 x); [−π, π]
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Rolle's Theorem
Date________________ Period____
For each problem, find the values of c that satisfy Rolle's Theorem. 1) y = x 2 + 4 x + 5; [−3, −1]
2) y = x 3 − 2 x 2 − x − 1; [−1, 2]
y
−8
−6
−4
y
8
8
6
6
4
4
2
2
−2
2
4
6
8 x
−8
3
7) y =
2− 3
2
−4
−4
−6
−6
−8
−8
{
7 2+ ,
7 3
7 2+ ,
7 3
{
{ 8) y =
{1 }
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3
7 2− ,
7 3
6
8 x
}
4+ 3
19 4 − ,
19 3
}
6) y = x 3 − x 2 − 4 x + 3; [−2, 2]
}
− x 2 − 2 x + 15 ; [−5, 3] −x + 4
2+
4
4) y = x 3 − 4 x 2 − x + 7; [−1, 4]
}
5) y = − x 3 + 2 x 2 + x − 1; [−1, 2]
{
−2 −2
3) y = − x 3 + 2 x 2 + x − 6; [−1, 2] 2−
−4
−2
{−2}
{
−6
1+ 3
13 1 − ,
13 3
}
x 2 − 2 x − 15 ; [−3, 5] −x + 6
{3 }
-1-
Worksheet by Kuta Software LLC
− x 2 + 2 x + 15 9) y = ; [−3, 5] x+4
x2 + x − 6 10) y = ; [−3, 2] −x + 3
{−1}
{3 −
11) y = −2sin (2 x); [−π, π]
{
−
3π π π 3π ,− , , 4 4 4 4
6}
12) y = sin (2 x); [−π, π]
}
{
−
3π π π 3π ,− , , 4 4 4 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 =
x 2 − x − 12 ; [−3, 4] x+4
{−4 + 2
2}
− x 2 + 36 15) y = ; [−6, 6] x+7
{−7 +
14) y =
{3 −
7}
−x2 + 4 16) y = ; [−2, 2] 4x
13 }
17) y = 2tan ( x); [−π, π]
−x2 − 2x + 8 ; [−4, 2] −x + 3
The function is not continuous on [−2, 2]
18) y = −2cos (2 x); [−π, π]
{
The function is not continuous on [−π, π]
π π − , 0, 2 2
}
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