Skip to main content
Editing a short answer - math & science question by WIRIS
You have permission to :
Edit this question
General
Category
Default for System (16649)
Test-Lidia
Question name
Question text
<div align="justify"><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif">Encuentre la ecuación principal de la recta tangente a la gráfica definida por:</span></font><br /><br /></div><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif"></span></font> <div align="center"><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif"></span><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#F«/mi»«/math»</span></span></span></span></span><span style="font-family: times new roman,times,serif"> <br /></span></font> <div align="justify"><font style="font-style: italic" size="4"><span style="font-family: times new roman,times,serif">la cual pasa por el punto </span><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P«/mi»«/math»</span></span></span></span>.</span></font><br style="font-family: times new roman,times,serif" /></div> <div style="text-align: center">#C1</div> <div style="text-align: center"></div> <div style="text-align: center" align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em></em></font></div> <div style="text-align: center" align="justify"><font color="#990000" size="4" face="times new roman,times,serif"><em>Obs.: La ecuación principal de la recta es de la forma <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«/math»</span></span></span></span></em></font></div> <div style="text-align: center" align="left"></div> <div style="text-align: center" align="justify"></div> <div style="text-align: center"></div> <div style="text-align: center"></div> <div style="text-align: center" align="center"></div> <div style="text-align: center" align="justify"><br /></div> <div style="text-align: center" align="justify"></div> <div style="text-align: center" align="justify"></div></div>
Default mark
General feedback
<i><font size="4" face="times new roman,times,serif"><span style="font-family: times new roman,times,serif">Solución:</span><br /><br /></font></i> <div style="text-align: justify; font-style: italic"><i><font size="4" face="times new roman,times,serif"><br /></font><font size="4" face="times new roman,times,serif"><span style="font-family: times new roman,times,serif"></span></font><font size="4" face="times new roman,times,serif"><span style="font-family: times new roman,times,serif"></span></font><font size="4" face="times new roman,times,serif"><span style="font-family: times new roman,times,serif"></span></font><font size="4" face="times new roman,times,serif"></font><font style="font-style: italic" size="4" face="times new roman,times,serif"><span style="font-family: times new roman,times,serif"></span></font><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif">Lo que buscamos es una recta de la forma:<br /><br /></font></i> <div align="center"><i><font size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«/math»</span></span></span></span><br /><br /></font></i></div><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif">Además tenemos que saber el valor de la derivada de una función en un punto puede interpretarse geométricamente, ya que corresponde a la pendiente de la recta tangente a la gráfica de la función en dicho punto.<br /><br /><br />Así que primero calcularemos la derivada de <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»</span></span></span></span>, ya que <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«/math»</span></span></span></span> evaluada en el punto <span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P«/mi»«/math»</span></span> es la pendiente <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«/math»</span></span></span></span> de la recta buscada.<br />Así:<br /><br /></font></i> <div align="center"><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#F«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#F1«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></span></font><font size="4" face="times new roman,times,serif"><br /></font></i> <div align="justify">Notación : <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»§apos;«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mrow»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math»</span></span></span></span><br /></div><i><font size="4" face="times new roman,times,serif"><br /></font></i> <div align="justify"><i><font size="4" face="times new roman,times,serif">Ahora evaluamos el punto </font><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P«/mi»«/math»</span></span> en <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»§apos;«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»#F1«/mi»«/math»</span></span></span></span>.<br /><br />Así:<br /></font></i> <div align="center"><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«mi»y«/mi»«mo»§apos;«/mo»«mfenced»«mrow»«mi»#p1«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»#pen«/mi»«/math»</span></span></span></span></font></i><br /></div><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><br /><br />Por lo tanto tenemos que </font><font size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»#pen«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»b«/mi»«/math»</span></span></span></span><br /><br />Ahora faltaría encontrar <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«/math»</span></span></span></span> para tener la ecuación de la recta. Para esto, reemplazamos el punto </font><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P«/mi»«/math»</span></span> en la ecuación anterior.<br /></font></i> <div align="center"><i><font size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mi»#p2«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#pen«/mi»«mo»·«/mo»«mi»#p11«/mi»«mo»+«/mo»«mi»b«/mi»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»#p2«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»#r3«/mi»«mo»+«/mo»«mi»b«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»/«/mo»«mo»+«/mo»«mfenced»«mi»#r4«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi»#p2«/mi»«mi»#c2«/mi»«mi»#r4«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»#r5«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»b«/mi»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«mtd»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></span><br /></font></i></div><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><br /><br />Por lo tanto la ecuación de la recta que es tangente a la gráfica de la función </font><font style="font-style: italic" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#fun«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#F«/mi»«/math»</span></span></span></span> y que pasa por el punto </font><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#P«/mi»«/math»</span></span> es:<br /></font></i> <div align="center"><i><font size="4" face="times new roman,times,serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»#pen«/mi»«mi»#x«/mi»«mi»#c3«/mi»«mi»#r5«/mi»«/math»</span></span></span></span><br /></font></i><font size="4" face="times new roman,times,serif"><i><br /></i></font> <div align="justify"><font size="4" face="times new roman,times,serif"><br />Gráficamente:<br /></font> <div align="center"><font size="4" face="times new roman,times,serif">#C3</font><br /></div></div></div></div></div><i><font style="font-style: italic; font-family: times new roman,times,serif" size="4" face="times new roman,times,serif"><br /><br /><br /><br /></font><font size="4" face="times new roman,times,serif"><br /><br /><br /><br /></font></i><br /><font size="4"><span style="font-family: times new roman,times,serif"></span></font><font size="4"><span style="font-family: times new roman,times,serif"></span></font></div>
No, case is unimportant
Yes, case must match
Correct answers
You must provide at least one possible answer. The first matching answer will be used to determine the score and feedback. Click the icon next to the answer field to edit the mathematical properties of the answer and the question.
Answer 1
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<i><font size="4" face="times new roman,times,serif">Bien. Continúa de esa manera.</font></i>
Answer 2
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<p align="justify"><font color="#000000" size="4" face="times new roman,times,serif"><em>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</em></font></p>
Answer 3
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Hint 2
Hint text
Created / last saved
Created
by
Admin User
on
Friday, 23 August 2013, 3:10 PM
Last saved
by
Admin User
on
Friday, 23 August 2013, 3:10 PM
There are required fields in this form marked
.