El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{3^{x} \left(2 x - 1\right) \left(x + 1\right)^{4}}{\sqrt{x}} \left(x - 3\right)^{6} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = -1$$
$$x_{2} = \frac{1}{2}$$
$$x_{3} = 3$$
Solución numérica$$x_{1} = -116.864539237352$$
$$x_{2} = -68.8123271393649$$
$$x_{3} = -101.23171116099$$
$$x_{4} = -85.7754776101862$$
$$x_{5} = -99.287879269485$$
$$x_{6} = -97.3469081858103$$
$$x_{7} = -93.4744630150122$$
$$x_{8} = -110.987321193058$$
$$x_{9} = -76.2708329325307$$
$$x_{10} = -87.6936572612594$$
$$x_{11} = -72.5212441745137$$
$$x_{12} = -80.0531966621338$$
$$x_{13} = -103.178201955389$$
$$x_{14} = -107.078442930151$$
$$x_{15} = -81.9547390140867$$
$$x_{16} = -118.826877251195$$
$$x_{17} = -70.6611138535694$$
$$x_{18} = -91.543508366471$$
$$x_{19} = -120.790688940089$$
$$x_{20} = -105.127168218336$$
$$x_{21} = -114.903766363755$$
$$x_{22} = -74.3915007204806$$
$$x_{23} = -112.944657790014$$
$$x_{24} = -95.4090206567306$$
$$x_{25} = -89.6164603051693$$
$$x_{26} = -66.9763024325075$$
$$x_{27} = -78.1583296069365$$
$$x_{28} = -109.031873697501$$
$$x_{29} = -83.8623457026723$$