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Lösning 1.3:1d - Versionshistorik
2026-05-25T02:54:45Z
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Tek den 29 juni 2010 kl. 11.56
2010-06-29T11:56:35Z
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<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 29 juni 2010 kl. 11.56</td>
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<tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_START</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">I punkterna <math>x=-\tfrac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">5}</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;"></math> och <math>x=\tfrac{1</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{2}</math> har funktionen kritiska punkter (se figuren nedan), dvs. derivata lika med noll, men notera att <math>x=-1</math> och <math>x=-\tfrac{1}{2}</math> inte är kritiska punkter (derivatan är inte ens definierad i dessa punkter).</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><center> <del style="color: red; font-weight: bold; text-decoration: none;">[[Bild</del>:<del style="color: red; font-weight: bold; text-decoration: none;">1_3_1d</del>-1<del style="color: red; font-weight: bold; text-decoration: none;">(2)</del>.<del style="color: red; font-weight: bold; text-decoration: none;">gif]] </del></center></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><center><ins style="color: red; font-weight: bold; text-decoration: none;">{{</ins>:<ins style="color: red; font-weight: bold; text-decoration: none;">1.3 </ins>- <ins style="color: red; font-weight: bold; text-decoration: none;">Figur - Grafen till övning </ins>1.<ins style="color: red; font-weight: bold; text-decoration: none;">3:1d med horisontella tangenter}}</ins></center></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_START</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center><small>Grafen har horisontella tangenter i ''x''&nbsp;=&nbsp;-5/2 och ''x''&nbsp;=&nbsp;1/2</small></center></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><<del style="color: red; font-weight: bold; text-decoration: none;">center</del>> <del style="color: red; font-weight: bold; text-decoration: none;">[[Bild:1_3_1d</del>-2<del style="color: red; font-weight: bold; text-decoration: none;">(2).gif]] </del></<del style="color: red; font-weight: bold; text-decoration: none;">center</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Funktionen har lokala minimipunkter i <math>x=-\tfrac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">5}</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;"></math>, <math>x=-\tfrac{1</ins>}{<ins style="color: red; font-weight: bold; text-decoration: none;">2}</math> och i den högra ändpunkten till definitionsintervallet <math>x=2</math>, och har lokala maximipunkter i den vänstra ändpunkten <math>x=-3</math>, i <math>x=-1</math> och <math>x=\tfrac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">1</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{2</ins>}<<ins style="color: red; font-weight: bold; text-decoration: none;">/math</ins>><ins style="color: red; font-weight: bold; text-decoration: none;">. Av dessa är <math>x=</ins>-<ins style="color: red; font-weight: bold; text-decoration: none;">1</math> global maximipunkt och <math>x=-\tfrac{5}{</ins>2<ins style="color: red; font-weight: bold; text-decoration: none;">}</ins></<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>> <ins style="color: red; font-weight: bold; text-decoration: none;">global minimipunkt.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Mellan de lokala extrempunkterna är funktionen strängt växande eller avtagande.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{<ins style="color: red; font-weight: bold; text-decoration: none;">| align="center"</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">||</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">{:1.3 - Figur - Grafen till övning 1.3:1d med avtagande område</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">| width="10px" |</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">||{{:1.3 - Figur - Grafen till övning 1.3:1d med växande område}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">|-</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">||<small>Område där funktionen är strängt avtagande</small></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">| width="10px" |</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">||<small>Område där funktionen är strängt växande</small></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">|</ins>}</div></td></tr>
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