WOLFRAM
|
DEMONSTRATIONS
PROJECT
Extreme Value Theorem
function
quadratic
trigonometric
cubic
purple
endpoint
orange
endpoint
Show
Show
Plot
[
4
-
16
Fri
2
Feb
2007
17
:
02
:
11
+
16
Fri
2
Feb
2007
17
:
02
:
11
2
,
{
Fri
2
Feb
2007
17
:
02
:
11
,
Min
[
-
3
,
2
]
-
1
,
Max
[
-
3
,
2
]
+
1
}
,
ColorFunctionScaling
False
,
ColorFunction
Function
[
{
ξ
$
,
ψ
$
}
,
If
[
(
ξ
$
-
-
3
)
(
ξ
$
-
2
)
<
0
,
Thick
,
Thin
]
]
]
,
,
,
PlotRangeClipping
False
,
ImageSize
{
400
,
300
}
If the function
f
is continuous over the closed interval
[
a
,
b
]
, then there is at least one maximum value (green) and one minimum value (red) of
f
in that interval.
