Rolle'S Theorem And The Mvt Worksheet 3.2 With Answers - Math 141e Calculus Maximus, Penn State School Page 2
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6Calculus Maximus
WS 3.2: Rolle’s Thm & MVT
[ ]
( )
(
)
1/ 3
2 / 3
= +
−
_____ 4. Determine if the function
f x
x x
1
x
satisfies the hypothesis of the MVT on
0,1 .
If it does, find all possible values of c satisfying the conclusion of the MVT. (You will have to
factor out least powers.)
2
(A)
3
1
(B)
4
1
(C)
2
1
(D)
3
(E) hypothesis not satisfied
_____ 5. Which of the following functions below satisfy the hypothesis of the MVT?
1
[ ]
( )
=
I.
f x
on
0, 2
+
x
1
[ ]
( )
1/ 3
=
II.
f x
x
on
0,1
[
]
( )
=
−
III.
f x
x
on
1,1
(A) I only
(B) I and II only
(C) I and III only
(D) II only
(E) II and III only
_____ 6. As a graduation present, Jenna received a sports car which she drives very fast but very, very
smoothly and safely. She always covers the 53 miles from her apartment in Austin, Texas to her
parents’ home in New Braunfels in less than 48 minutes. To slow her down, her dad decides to
change the speed limit (he has connections.) Which one of the speed limits below is the highest
speed her father can post, but still catch her speeding at some point on her trip?
(A) 55 mph
(B) 70 mph
(C) 65 mph
(D) 50 mph
(E) 60 mph
_____ 7. Consider the following statements:
[ ]
( )
I.
f x is continuous on
, a b
( )
(
)
II.
f x is differentiable on
, a b
( )
( )
=
III.
f a
f b
(
)
∈
Which of the above statements are required in order to guarantee a
c
a b
,
such that
( )
( )
( )
′
−
=
−
f c b a
(
)
f b
f a
?
(A) I only (B) I and II only
(C) I, II, and III
(D) III only
(E) I and III only
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