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Let us consider the function <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»:«/mo»«msup»«mi»§#8477;«/mi»«mn»2«/mn»«/msup»«mo»§#8594;«/mo»«msup»«mi»§#8477;«/mi»«mn»2«/mn»«/msup»«/math»</span>, <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»§#8712;«/mo»«msup»«mi»C«/mi»«mn»1«/mn»«/msup»«mfenced»«msup»«mi»§#8477;«/mi»«mn»2«/mn»«/msup»«/mfenced»«/math»</span> which complies that <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mi»#a«/mi»«/math»</span> , and the surface <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«/math»</span> defined by the equation <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»xz«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mi»zg«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mi»#b«/mi»«/msup»«mo»+«/mo»«msup»«mi»y«/mi»«mi»#b«/mi»«/msup»«mo»+«/mo»«msup»«mi»z«/mi»«mn»2«/mn»«/msup»«/math»</span>.<br /><br />Knowing that this equation defines <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«/math»</span> in a neighbourhood of the point <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»,«/mo»«mi»#a«/mi»«/mrow»«/mfenced»«/math»</span>, the conditions that must meet the differential of <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«/math»</span> in order to <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«/math»</span> has a critical point at the origin.<br /><br />The solution must be expressed according to the following criteria<br /><br /> <div style="text-align: center;"> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»§#8706;«/mo»«mi»g«/mi»«/mrow»«mrow»«mo»§#8706;«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mo»§#8706;«/mo»«mi»g«/mi»«/mrow»«mrow»«mo»§#8706;«/mo»«mi»y«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/math»</span><br /></div><br /> <div style="text-align: center;"> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mo»§nbsp;«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/math»</span><br /></div><br />
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Answer 1
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66.66667%
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33.33333%
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16.66667%
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11.11111%
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Answer 2
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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%
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100%
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33.33333%
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Thursday, 10 December 2015, 10:53 AM
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Thursday, 10 December 2015, 10:53 AM
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