Chapter 3
–
Mean Value Theorem WKST
Name:
Understanding IVT, MVT, and Rolle’s Theorem
A Graphing Calculator is allowed for these problems.
For problems #1 and #2, find the value of
c
guaranteed by the Mean Value Theorem on the indicated interval such that
.
1. on [ 1 , 3 ] 2. on [ 1 , 1 ]
3.
Which of the following satisfy the hypotheses of Mean Value Theorem on the interval [ 0 , 2 ] ?
I.
II.
III.
4. Which of the following satisfy the hypotheses of Mean Value Theorem on the interval [ 0 , 3 ] ? Note: this is the same as #3, except the interval is different. I. II. III.
a
b
a
f
b
f
c
f


=
)
(
)
(
)
(
'
2
)
(
x
x
f
=
1
)
(
3
+
=
x
x
f
x
x
x
f
2
cos
sin
)
(
+
p
=
3
2
)
(

=
x
x
f
x
x
x
f
2
)
(
2

=
x
x
x
f
2
cos
sin
)
(
+
p
=
3
2
)
(

=
x
x
f
x
x
x
f
2
)
(
2

=
5. Which of the following satisfy the hypotheses of Rolle’s Theorem on the interval [ 0 , 2 ] ? I. II. III. IV.
6. Let fbe continuous for where ( 0 , 13 ) and ( 5 , 3 ) are the endpoints of f. The Intermediate Value Theorem guarantees which of the following?