Los puntos críticos y de inflexión de la función $G(x) = x^4 + 2x^3 - 3x^2 - 4x$ son los siguientes:

• Puntos críticos (extremos locales):

  • $x = -2$, $G(-2) = -4$
  • $x = -\frac{1}{2}$, $G\left(-\frac{1}{2}\right) = \frac{17}{16}$
  • $x = 1$, $G(1) = -4$

• Puntos de inflexión:

  • $x_1 = -\frac{1}{2} + \frac{\sqrt{3}}{2}$
  • $x_2 = -\frac{\sqrt{3}}{2} - \frac{1}{2}$

Ahora generaré el gráfico del plano cartesiano mostrando los puntos críticos y de inflexión.It seems like I can’t do more advanced data analysis right now. Please try again later.

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1. Would you like a step-by-step explanation on how to find critical points?
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Tip: The sign of the second derivative at critical points helps to identify if they are maxima, minima, or saddle points.