Rolle'S Theorem And The Mvt Worksheet 3.2 With Answers - Math 141e Calculus Maximus, Penn State School Page 3
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6Calculus Maximus
WS 3.2: Rolle’s Thm & MVT
Short Answer
8. Without looking at your notes, state the Mean Value Theorem.
If . . .
then . . .
9. Determine if Rolle’s Theorem can be applied to the following functions on the given interval. If so, find
the value(s) guaranteed by the theorem.
2
π π
−
−
⎡
⎤
x
2
x
3
[
]
( )
( )
=
− ⎢
=
−
(a)
f x
cos 2
x
on
,
(b)
g x
on
1,3
⎥
+
⎣
12 6
⎦
x
2
10. Determine if the MVT can be applied to the following functions on the given interval. If so, find the
exact value(s) guaranteed by the theorem. Be sure to show your set up in finding the value(s).
− ≤ <
⎧
arcsin ,
x
1
x
1
⎪
[ ]
[
]
( )
(
)
( )
=
−
−
= ⎨
(a)
on
(b)
on
.
f x
ln
x
1
2, 4
f x
1,3
x
≤ ≤
, 1
x
3
⎪ ⎩
2
+
⎡
⎤
x
1
1
( )
[
]
( )
π
=
=
+
(c)
g x
on
, 2
(d)
f x
2sin
x
sin 2
x
on
0,
⎢
⎥
x
⎣
2
⎦
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