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inflection (2-x^2)/(1+x^4)

Solución

puntos de inflexión

\frac{2 - x ^{2}}{1 + x ^{4}}

(- \frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}}), (- \frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}), (\frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}), (\frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}})

Pasos de solución

Encontrar dónde

f^{''} (x)

es igual a cero o no está definido

x = - \frac{7.14711 E 15}{1.0 E 15}, x = - \frac{2.98799 E 15}{5.0 E 15}, x = \frac{2.98799 E 15}{5.0 E 15}, x = \frac{7.14711 E 15}{1.0 E 15}

Identificar puntos de inflexión que no estén en el dominio o donde

f (x)

no es continuo

Dominio de

\frac{2 - x ^{2}}{1 + x ^{4}} : - \infty < x < \infty

Todos los puntos de inflexión estan en el dominio y no en los bordes del dominio

x = - \frac{7.14711 E 15}{1.0 E 15}, x = - \frac{2.98799 E 15}{5.0 E 15}, x = \frac{2.98799 E 15}{5.0 E 15}, x = \frac{7.14711 E 15}{1.0 E 15}

Find intervals:

Concavo hacia abajo

: - \infty < x < - \frac{7.14711 E 15}{1.0 E 15},

Concavo hacia arriba

: - \frac{7.14711 E 15}{1.0 E 15} < x < - \frac{2.98799 E 15}{5.0 E 15},

Concavo hacia abajo

: - \frac{2.98799 E 15}{5.0 E 15} < x < \frac{2.98799 E 15}{5.0 E 15},

Concavo hacia arriba

: \frac{2.98799 E 15}{5.0 E 15} < x < \frac{7.14711 E 15}{1.0 E 15},

Concavo hacia abajo

: \frac{7.14711 E 15}{1.0 E 15} < x < \infty

Ingrese

x = - \frac{7.14711 E 15}{1.0 E 15}

\frac{2 - x ^{2}}{1 + x ^{4}} : - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}}

(- \frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}})

Ingrese

x = - \frac{2.98799 E 15}{5.0 E 15}

\frac{2 - x ^{2}}{1 + x ^{4}} : \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}

(- \frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}})

Ingrese

x = \frac{2.98799 E 15}{5.0 E 15}

\frac{2 - x ^{2}}{1 + x ^{4}} : \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}

(\frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}})

Ingrese

x = \frac{7.14711 E 15}{1.0 E 15}

\frac{2 - x ^{2}}{1 + x ^{4}} : - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}}

(\frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}})

(- \frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}}), (- \frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}), (\frac{2.98799 E 15}{5.0 E 15}, \frac{3.50601 E 31}{5.0 E 1 5 ^{2} + 2.98799 E 1 5 ^{2}}), (\frac{7.14711 E 15}{1.0 E 15}, - \frac{5.14711 E 30}{1.0 E 1 5 ^{2} + 7.14711 E 1 5 ^{2}})

f (x) = \frac{5 x - 10}{x ^{2} + x - 12}

f (x) = (\frac{7}{x}) + (\frac{1}{x ^{2}})

f (x) = \frac{5}{- x ^{2} - 3 x + 4}

(- 6, 6), (2, - 4)

y = x + 7