Rolle'S Theorem And The Mvt Worksheet 3.2 With Answers - Math 141e Calculus Maximus, Penn State School
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6Calculus Maximus
WS 3.2: Rolle’s Thm & MVT
Name_________________________________________ Date________________________ Period______
Worksheet 3.2—Rolle’s Theorem and the MVT
Show all work. No calculator unless otherwise stated.
Multiple Choice
( )
=
−
_____ 1. Determine if the function
f x
x
6
x
satisfies the hypothesis of Rolle’s Theorem on the
[ ]
interval
0,6 , and if it does, find all numbers c satisfying the conclusion of that theorem.
(A) 2, 3
(B) 4, 5
(C) 5
(D) 4
(E) hypothesis not satisfied
[
]
( )
( )
−
− =
_____ 2. Let f be a function defined on
1,1
such that
f
1
f
1
. Consider the following properties
that f might have:
[
]
(
)
−
−
I.
f is continuous on
, differentiable on
.
1,1
1,1
( )
3
=
II.
f x
cos
x
( )
π
=
III.
f x
sin
x
(
)
( )
′
−
= ?
Which properties ensure that there exists a c in
1,1
at which
f c
0
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
[
]
( )
3
=
− −
−
_____ 3. Determine if the function
f x
x
x
1
satisfies the hypothesis of the MVT on
1, 2
. If it
does, find all possible values of c satisfying the conclusion of the MVT.
1
−
(A)
2
−
(B) 1, 1
(C) 0
(D) 1
(E) hypothesis not satisfied
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