Topic
: Intermediate value theorem with an interval
Question
: Which of the following statements is true?
Answer choices
:
A
The Intermediate Value Theorem only applies to discontinuous
functions.
B
The Intermediate Value Theorem only applies when there is no
interval.
C
The Intermediate Value Theorem only applies when there is an open
interval.
D
The Intermediate Value Theorem only applies when there is a
closed interval.
88

Solution
: D
The Intermediate Value Theorem states that for a function on a closed
interval
[
a
,
b
]
where the function is continuous on the interval, a point
c
exists on the interval where
f
(
c
) =
k
.
f
(
a
) <
k
<
f
(
b
)
and
a
<
c
<
b
89