El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$3^{x} - \frac{1}{x^{3}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{3 W\left(\frac{\log{\left(3 \right)}}{3}\right)}{\log{\left(3 \right)}}$$
Solución numérica$$x_{1} = -25362.5803223436$$
$$x_{2} = -10105.8084969239$$
$$x_{3} = -37229.0173858502$$
$$x_{4} = -33838.605204445$$
$$x_{5} = -18581.7718990583$$
$$x_{6} = -34686.2081625031$$
$$x_{7} = -26210.1823018004$$
$$x_{8} = -11800.9927225258$$
$$x_{9} = -32143.3994905401$$
$$x_{10} = -22819.7753899021$$
$$x_{11} = -35533.8111815333$$
$$x_{12} = 0.757696978830077$$
$$x_{13} = -13496.1823773059$$
$$x_{14} = -23667.3768483792$$
$$x_{15} = -24514.9784989468$$
$$x_{16} = -27905.3866720051$$
$$x_{17} = -32991.0023120587$$
$$x_{18} = -31295.7967456477$$
$$x_{19} = -38076.6205637343$$
$$x_{20} = -30448.1940837816$$
$$x_{21} = -28752.9890385016$$
$$x_{22} = -29600.5915120748$$
$$x_{23} = -27057.7844226494$$
$$x_{24} = -20276.9724079398$$
$$x_{25} = -14343.7788633668$$
$$x_{26} = -16886.5729892823$$
$$x_{27} = -41467.0337078697$$
$$x_{28} = -38924.2237877047$$
$$x_{29} = -39771.8270548144$$
$$x_{30} = -42314.6370890542$$
$$x_{31} = -36381.4142572736$$
$$x_{32} = -12648.5869274109$$
$$x_{33} = -19429.3719797754$$
$$x_{34} = -10953.3999636623$$
$$x_{35} = -40619.4303623627$$
$$x_{36} = -16038.9742925398$$
$$x_{37} = -15191.3762140447$$
$$x_{38} = -17734.1722156161$$
$$x_{39} = -9258.21575568866$$
$$x_{40} = -21124.5731417223$$
$$x_{41} = -21972.1741457489$$