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(Section 2.8: Continuity)
2.8.15
PART H: THE INTERMEDIATE VALUE THEOREM (IVT)
Example 13
Examine the graph of
fx
()
=
x
2
on the
x
interval
0, 2
±
²
³
´
.
(Figure 2.8.n)
f
0
=
0
, and
f
2
=
4
. Observe that every function value between 0 and 4
is taken on by
f
at some
x
value in
0, 2
±
²
³
´
. This is guaranteed by the fact
that
f
is continuous on
0, 2
±
²
³
´
. More generally …
The Intermediate Value Theorem (IVT): Informal Statement
If a function
f
is continuous on a closed interval
a
,
b
±
²
³
´
,
then
f
takes on every real value between
fa
and
fb
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 sturst
 Continuity, Intermediate Value Theorem

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