Antwort 1.3:1

Aus Online Mathematik Brückenkurs 2

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(Translated into English)
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{| cellspacing="10px"
{| cellspacing="10px"
||a)
||a)
-
||Kritisk&nbsp;punkt:||<math>x=0</math>
+
||Critical&nbsp;point:||<math>x=0</math>
|-
|-
||
||
-
||Terasspunkt:||Saknas
+
||Inflexion&nbsp;point:||None
|-
|-
||
||
-
||Lokalt&nbsp;min:||<math>x=0</math>
+
||Local&nbsp;min:||<math>x=0</math>
|-
|-
||
||
-
||Lokalt&nbsp;max:||Saknas
+
||Local&nbsp;max:||None
|-
|-
||
||
-
||Globalt&nbsp;min:||<math>x=0</math>
+
||Global&nbsp;min:||<math>x=0</math>
|-
|-
||
||
-
||Globalt&nbsp;max:||Saknas
+
||Global&nbsp;max:||None
|-
|-
||
||
-
||Strängt&nbsp;väx.:||<math>x\ge0</math>
+
||Strictly&nbsp;incr.:||<math>x\ge0</math>
|-
|-
||
||
-
||Strängt&nbsp;avt.:||<math>x\le0</math>
+
||Strictly&nbsp;decr.:||<math>x\le0</math>
|}
|}
| width="50%" valign="top" |
| width="50%" valign="top" |
{| cellspacing="10px"
{| cellspacing="10px"
||b)
||b)
-
||Kritisk&nbsp;punkt:||<math>x=-1</math>, <math>x=1</math>
+
||Critical&nbsp;point:||<math>x=-1</math>, <math>x=1</math>
|-
|-
||
||
-
||Terasspunkt:||Saknas
+
||Inflexion&nbsp;point:||None
|-
|-
||
||
-
||Lokalt&nbsp;min:||<math>x=-3</math>, <math>x=1</math>
+
||Local&nbsp;min:||<math>x=-3</math>, <math>x=1</math>
|-
|-
||
||
-
||Lokalt&nbsp;max:||<math>x=-1</math>, <math>x=2</math>
+
||Local&nbsp;max:||<math>x=-1</math>, <math>x=2</math>
|-
|-
||
||
-
||Globalt&nbsp;min:||<math>x=-3</math>
+
||Global&nbsp;min:||<math>x=-3</math>
|-
|-
||
||
-
||Globalt&nbsp;max:||<math>x=-1</math>
+
||Global&nbsp;max:||<math>x=-1</math>
|-
|-
||
||
-
||Strängt&nbsp;väx.:||<math>[-3,-1]</math>, <math>[1,2]</math>
+
||Strictly&nbsp;incr.:||<math>[-3,-1]</math>, <math>[1,2]</math>
|-
|-
||
||
-
||Strängt&nbsp;avt.:||<math>[-1,1]</math>
+
||Strictly&nbsp;decr.:||<math>[-1,1]</math>
|}
|}
|-
|-
Zeile 56: Zeile 56:
{| cellspacing="10px"
{| cellspacing="10px"
| valign="top" |c)
| valign="top" |c)
-
| valign="top" |Kritisk punkt:
+
| valign="top" |Critical point:
| valign="top" |<math>x=-2</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
| valign="top" |<math>x=-2</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Terasspunkt:||<math>x=-1</math>
+
||Inflexion&nbsp;point:||<math>x=-1</math>
|-
|-
||
||
-
||Lokalt&nbsp;min:||<math>x=-2</math>, <math>x=2</math>
+
||Local&nbsp;min:||<math>x=-2</math>, <math>x=2</math>
|-
|-
||
||
-
||Lokalt&nbsp;max:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
+
||Local&nbsp;max:||<math>x=-3</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Globalt&nbsp;min:||<math>x=-2</math>
+
||Global&nbsp;min:||<math>x=-2</math>
|-
|-
||
||
-
||Globalt&nbsp;max:||<math>x=-3</math>
+
||Global&nbsp;max:||<math>x=-3</math>
|-
|-
||
||
-
||Strängt&nbsp;väx.:||<math>[-2,\tfrac{1}{2}]</math>
+
||Strictly&nbsp;incr.:||<math>[-2,\tfrac{1}{2}]</math>
|-
|-
||
||
-
||Strängt&nbsp;avt.:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
+
||Strictly&nbsp;decr.:||<math>[-3,-2]</math>, <math>[\tfrac{1}{2},2]</math>
|}
|}
| width="50%" valign="top" |
| width="50%" valign="top" |
{| cellspacing="10px"
{| cellspacing="10px"
| valign="top" |d)
| valign="top" |d)
-
| valign="top" |Kritisk&nbsp;punkt:
+
| valign="top" |Critical&nbsp;point:
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=\tfrac{1}{2}</math>
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Terasspunkt:||Saknas
+
||Inflexion&nbsp;point:||None
|-
|-
||
||
-
| valign="top" |Lokalt&nbsp;min:
+
| valign="top" |Local&nbsp;min:
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=-\tfrac{1}{2}</math>, <math>x=2</math>
| valign="top" |<math>x=-\tfrac{5}{2}</math>, <math>x=-\tfrac{1}{2}</math>, <math>x=2</math>
|-
|-
||
||
-
| valign="top" |Lokalt&nbsp;max:
+
| valign="top" |Local&nbsp;max:
| valign="top" |<math>x=-3</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
| valign="top" |<math>x=-3</math>, <math>x=-1</math>, <math>x=\tfrac{1}{2}</math>
|-
|-
||
||
-
||Globalt&nbsp;min:||<math>x=-\tfrac{5}{2}</math>
+
||Global&nbsp;min:||<math>x=-\tfrac{5}{2}</math>
|-
|-
||
||
-
||Globalt&nbsp;max:||<math>x=-1</math>
+
||Global&nbsp;max:||<math>x=-1</math>
|-
|-
||
||
-
| valign="top" |Strängt&nbsp;väx.:
+
| valign="top" |Strictly&nbsp;incr.:
| valign="top" |<math>[-\tfrac{5}{2},-1]</math>, <math>[-\tfrac{1}{2},\tfrac{1}{2}]</math>
| valign="top" |<math>[-\tfrac{5}{2},-1]</math>, <math>[-\tfrac{1}{2},\tfrac{1}{2}]</math>
|-
|-
||
||
-
| valign="top" |Strängt&nbsp;avt.:
+
| valign="top" |Strictly&nbsp;decr.:
| valign="top" |<math>[-3,-\tfrac{5}{2}]</math>, <math>[-1,-\tfrac{1}{2}]</math>, <math>[\tfrac{1}{2},2]</math>
| valign="top" |<math>[-3,-\tfrac{5}{2}]</math>, <math>[-1,-\tfrac{1}{2}]</math>, <math>[\tfrac{1}{2},2]</math>
|}
|}
|}
|}

Version vom 07:21, 3. Sep. 2008

a) Critical point:\displaystyle x=0
Inflexion point:None
Local min:\displaystyle x=0
Local max:None
Global min:\displaystyle x=0
Global max:None
Strictly incr.:\displaystyle x\ge0
Strictly decr.:\displaystyle x\le0
b) Critical point:\displaystyle x=-1, \displaystyle x=1
Inflexion point:None
Local min:\displaystyle x=-3, \displaystyle x=1
Local max:\displaystyle x=-1, \displaystyle x=2
Global min:\displaystyle x=-3
Global max:\displaystyle x=-1
Strictly incr.:\displaystyle [-3,-1], \displaystyle [1,2]
Strictly decr.:\displaystyle [-1,1]
c) Critical point: \displaystyle x=-2, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
Inflexion point:\displaystyle x=-1
Local min:\displaystyle x=-2, \displaystyle x=2
Local max:\displaystyle x=-3, \displaystyle x=\tfrac{1}{2}
Global min:\displaystyle x=-2
Global max:\displaystyle x=-3
Strictly incr.:\displaystyle [-2,\tfrac{1}{2}]
Strictly decr.:\displaystyle [-3,-2], \displaystyle [\tfrac{1}{2},2]
d) Critical point: \displaystyle x=-\tfrac{5}{2}, \displaystyle x=\tfrac{1}{2}
Inflexion point:None
Local min: \displaystyle x=-\tfrac{5}{2}, \displaystyle x=-\tfrac{1}{2}, \displaystyle x=2
Local max: \displaystyle x=-3, \displaystyle x=-1, \displaystyle x=\tfrac{1}{2}
Global min:\displaystyle x=-\tfrac{5}{2}
Global max:\displaystyle x=-1
Strictly incr.: \displaystyle [-\tfrac{5}{2},-1], \displaystyle [-\tfrac{1}{2},\tfrac{1}{2}]
Strictly decr.: \displaystyle [-3,-\tfrac{5}{2}], \displaystyle [-1,-\tfrac{1}{2}], \displaystyle [\tfrac{1}{2},2]
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