Cálculo/Prueba 2-Medianas P2-CII-Plano Tangente 4 - M Pregunta: CII-PT4-Eval2-M

Dada la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»C«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«mn»2«/mn»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»C«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«/math».

Determine el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«msub»«mi»x«/mi»«mn»0«/mn»«/msub»«mo»,«/mo»«msub»«mi»y«/mi»«mn»0«/mn»«/msub»«mo»)«/mo»«/math» tal que el plano tangente sea horizontal.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»0«/mn»«/msub»«mo»=«/mo»«/math»{#1}
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»y«/mi»«mn»0«/mn»«/msub»«mo»=«/mo»«/math»{#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>D</mi><mo>=</mo><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mn>2</mn><mo>*</mo><mi>A1</mi></mtd><mtd><mi>B1</mi></mtd></mtr><mtr><mtd><mi>B1</mi></mtd><mtd><mn>2</mn><mo>*</mo><mi>A2</mi></mtd></mtr></mtable></mfenced></mfenced></mrow><mrow><mi>D</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mo>-</mo><mi>C1</mi></mtd><mtd><mi>B1</mi></mtd></mtr><mtr><mtd><mo>-</mo><mi>C2</mi></mtd><mtd><mn>2</mn><mo>*</mo><mi>A2</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mfenced close="|" open="|"><mfenced><mtable><mtr><mtd><mn>2</mn><mo>*</mo><mi>A1</mi></mtd><mtd><mo>-</mo><mi>C1</mi></mtd></mtr><mtr><mtd><mi>B1</mi></mtd><mtd><mo>-</mo><mi>C2</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>:</mo><mo>=</mo><mi>aux1</mi><mo>/</mo><mi>D</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>:</mo><mo>=</mo><mi>aux2</mi><mo>/</mo><mi>D</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>364</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>9</mn><mn>182</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>91</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>