document.write( "Question 1176786: Mediante GeoGebra obtener raíces, puntos máximos y mínimos, así como las gráficas de las siguientes funciones.\r
\n" ); document.write( "\n" ); document.write( " p(x)=x^3 -7 x^2+15x-9
\n" ); document.write( " p(x)=x^4+ x^3 -4 x^2-4x
\n" ); document.write( " p(x)=x^5-10x^3 +9x
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #804295 by MathLover1(20855)\"\" \"About 
You can put this solution on YOUR website!
1.\r
\n" ); document.write( "\n" ); document.write( "\"p%28x%29=x%5E3+-7x%5E2%2B15x-9\".......factor completamente
\n" ); document.write( "\"p%28x%29=x%5E3+-x%5E2-6x%5E2%2B6x%2B9x-9\"
\n" ); document.write( "\"p%28x%29=%28x%5E3+-x%5E2%29-%286x%5E2-6x%29%2B%289x-9%29\"
\n" ); document.write( "\"p%28x%29=x%5E2%28x+-1%29-6x%28x-1%29%2B9%28x-1%29\"
\n" ); document.write( "\"p%28x%29+=+%28x%5E2+-+6x%2B9%29+%28x+-+1%29\"
\n" ); document.write( "\"p%28x%29+=+%28x+-+3%29%5E2+%28x+-+1%29\"\r
\n" ); document.write( "\n" ); document.write( "soluciones:
\n" ); document.write( "\"%28x+-+3%29%5E2+%28x+-+1%29=0\"\r
\n" ); document.write( "\n" ); document.write( "si \"%28x+-+3%29%5E2+=0+\"=>\"%28x+-+3%29+=0\" =>\"x+=3\"
\n" ); document.write( "si \"%28x+-+1%29=0+\"=> \"x=1\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Suppose that x=c is a critical point of f (x ) then:
\n" ); document.write( "If f'(x)>0 to the left of x=c and f' (x )<0 to the right of x=c then x=c is a local maximum.
\n" ); document.write( "If f'(x) < 0 to the left of x=c and f' (x )>0 to the right of x=c then x=c is a local minimum.
\n" ); document.write( "If f (x ) is the same sign on both sides of x=c then x=c is neither a local maximum nor a local minimum.\r
\n" ); document.write( "\n" ); document.write( "Suponga que x = c es un punto crítico de f (x) entonces:
\n" ); document.write( "Si f '(x)> 0 a la izquierda de x = c y f' (x) <0 a la derecha de x = c, entonces x = c es un máximo local.
\n" ); document.write( "Si f '(x) <0 a la izquierda de x = c y f' (x)> 0 a la derecha de x = c, entonces x = c es un mínimo local.
\n" ); document.write( "Si f (x) es el mismo signo en ambos lados de x = c, entonces x = c no es ni un máximo local ni un mínimo local.\r
\n" ); document.write( "\n" ); document.write( "entonces, encuentre la primera derivada de la función p (x)\r
\n" ); document.write( "\n" ); document.write( "\"p\"'\"%28x%29=3x%5E2+-14x%2B15\"
\n" ); document.write( "\"3x%5E2+-14x%2B15=0\"
\n" ); document.write( "\"%28x+-+3%29+%283+x+-+5%29+=+0\"\r
\n" ); document.write( "\n" ); document.write( "\"x-3=0\" ->\"x=3\"
\n" ); document.write( "\"3x-5=0+\"-> \"x=5%2F3\"\r
\n" ); document.write( "\n" ); document.write( "ahora encuentra\r
\n" ); document.write( "\n" ); document.write( "\"p%28x%29=x%5E3+-7x%5E2%2B15x-9\" if \"x=3\"
\n" ); document.write( "\"p%283%29=3%5E3+-7%2A3%5E2%2B15%2A3-9=0\"\r
\n" ); document.write( "\n" ); document.write( "(\"3\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "and if \"x=5%2F3\"\r
\n" ); document.write( "\n" ); document.write( "\"p%285%2F3%29=%285%2F3%29%5E3+-7%2A%285%2F3%29%5E2%2B15%2A%285%2F3%29-9=32%2F27\"
\n" ); document.write( "(\"5%2F3\",\"32%2F27\")\r
\n" ); document.write( "\n" ); document.write( "entonces usted tiene\r
\n" ); document.write( "\n" ); document.write( "Maximum: (\"5%2F3\",\"32%2F27\")
\n" ); document.write( "Minimum:(\"3\",\"0\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "\"p%28x%29=x%5E4%2B+x%5E3+-4+x%5E2-4x\"
\n" ); document.write( "\"p%28x%29+=+x+%28x%5E3+%2B+x%5E2+-+4+x+-+4%29\"
\n" ); document.write( "\"p%28x%29+=+x+%28%28x%5E3+%2B+x%5E2%29+-+%284+x%2B+4%29%29\"
\n" ); document.write( "\"p%28x%29+=+x+%28x%5E2%28x+%2B+1%29+-+4%28x%2B+1%29%29\"
\n" ); document.write( "\"p%28x%29+=+x+%28%28x%5E2+-+4%29%28x%2B+1%29%29\"
\n" ); document.write( "\"p%28x%29+=+x%28x+-+2%29%28x+%2B+2%29%28x+%2B+1%29\"
\n" ); document.write( "soluciones:
\n" ); document.write( "\"x=0\"
\n" ); document.write( "\"x=2\"
\n" ); document.write( "\"x=-2\"
\n" ); document.write( "\"x=-1\"\r
\n" ); document.write( "\n" ); document.write( "\"p\"'\"%28x%29=4x%5E3%2B+3x%5E2+-8x-4\"
\n" ); document.write( "\"4x%5E3%2B+3x%5E2+-8x-4=0\"\r
\n" ); document.write( "\n" ); document.write( "usando la calculadora obtendrás\r
\n" ); document.write( "\n" ); document.write( "\"x\"\"-1.61\"\r
\n" ); document.write( "\n" ); document.write( "\"x\"\"-0.47\"\r
\n" ); document.write( "\n" ); document.write( "\"x\"\"1.33\"\r
\n" ); document.write( "\n" ); document.write( "\"p%28-1.61%29=%28-1.61%29%5E4%2B+%28-1.61%29%5E3+-4+%2A%28-1.61%29%5E2-4%2A%28-1.61%29=-1.38\"->(\"-1.61\",\"-1.38\")
\n" ); document.write( "\"p%28-0.47%29=%28-0.47%29%5E4%2B+%28-0.47%29%5E3+-4+%2A%28-0.47%29%5E2-4%2A%28-0.47%29=0.94\"->(\"-0.47\",\"0.94\")
\n" ); document.write( "\"p%281.33%29=%281.33%29%5E4%2B+%281.33%29%5E3+-4+%2A%281.33%29%5E2-4%2A%281.33%29=-6.91\"->(\"1.33\",\"-6.91\")\r
\n" ); document.write( "\n" ); document.write( "Maximum:(\"-0.47\",\"0.94\")
\n" ); document.write( "Minimum:(\"1.33\",\"-6.91\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3.
\n" ); document.write( "\"p%28x%29=x%5E5-10x%5E3+%2B9x\"
\n" ); document.write( "\"p%28x%29=x%28x%5E4-10x%5E2+%2B9%29\"
\n" ); document.write( "\"p%28x%29=x%28x%5E4-x%5E2-9x%5E2+%2B9%29\"
\n" ); document.write( "\"p%28x%29=x%28%28x%5E4-x%5E2%29-%289x%5E2+-9%29%29\"
\n" ); document.write( "\"p%28x%29=x%28x%5E2%28x%5E2-1%29-9%28x%5E2+-1%29%29\"
\n" ); document.write( "\"p%28x%29=x%28%28x%5E2-9%29%28x%5E2+-1%29%29\"
\n" ); document.write( "\"p%28x%29=x%28%28x%5E2-3%5E2%29%28x%5E2+-1%29%29\"
\n" ); document.write( "\"p%28x%29=x%28x-3%29%28x%2B3%29%28x+-1%29%28x%2B1%29\"\r
\n" ); document.write( "\n" ); document.write( "=> soluciones:\r
\n" ); document.write( "\n" ); document.write( "\"x=0\"
\n" ); document.write( "\"x=3\"
\n" ); document.write( "\"x=-3\"
\n" ); document.write( "\"x=1\"
\n" ); document.write( "\"x=-1\"\r
\n" ); document.write( "\n" ); document.write( "\"p\"'\"%28x%29=5x%5E4-30x%5E2+%2B9\"
\n" ); document.write( "\"5x%5E4-30x%5E2+%2B9=0\"
\n" ); document.write( "\"5x%5E4-30x%5E2+%2B9=0\"\r
\n" ); document.write( "\n" ); document.write( "usando la calculadora obtendrás\r
\n" ); document.write( "\n" ); document.write( "\"x+=+sqrt%283+-+6%2Fsqrt%285%29%29\"\"x=0.56\"
\n" ); document.write( "\"x+=+-sqrt%283+-+6%2Fsqrt%285%29%29\"\"x=-0.56\"
\n" ); document.write( "\"x+=+sqrt%283%2B6%2Fsqrt%285%29%29\"\"x=2.38\"
\n" ); document.write( "\"x+=+-sqrt%283+%2B+6%2Fsqrt%285%29%29\"\"x=-2.38\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"p%280.56%29=%280.56%29%5E5-10%2A%280.56%29%5E3+%2B9%280.56%29=3.34\" ->(\"0.56\",\"3.34\")
\n" ); document.write( "\"p%28-0.56%29=%28-0.56%29%5E5-10%2A%28-0.56%29%5E3+%2B9%28-0.56%29=-3.34\" ->(\"-0.56\",\"-3.34\")
\n" ); document.write( "\"p%282.38%29=%282.38%29%5E5-10%2A%282.38%29%5E3+%2B9%282.38%29=-37.03\" ->(\"2.38\",\"-37.03\")
\n" ); document.write( "\"p%28-2.38%29=%28-2.38%29%5E5-10%2A%28-2.38%29%5E3+%2B9%28-2.38%29=37.03\" ->(\"-2.38\",\"37.03\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Maximum:(\"0.56\",\"3.34\") y (\"-0.56\",\"-3.34\")
\n" ); document.write( "Minimum:(\"2.38\",\"-37.03\") y (\"2.38\",\"-37.03\")\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );