Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{- x} x^{3} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = 113.817945104066$$
$$x_{2} = 80.1510345473422$$
$$x_{3} = 47.2258221026002$$
$$x_{4} = 90.0216356011828$$
$$x_{5} = 105.873885239726$$
$$x_{6} = 117.793236913112$$
$$x_{7} = 66.4179766096377$$
$$x_{8} = 49.0998156927321$$
$$x_{9} = 74.2498293547747$$
$$x_{10} = 93.9790749415684$$
$$x_{11} = 86.0690060516037$$
$$x_{12} = 45.3699033599292$$
$$x_{13} = 78.181864782784$$
$$x_{14} = 76.2147268831127$$
$$x_{15} = 72.2874103791773$$
$$x_{16} = 82.1220528473812$$
$$x_{17} = 101.905718658495$$
$$x_{18} = 107.858996843108$$
$$x_{19} = 54.8012720585185$$
$$x_{20} = 52.8897741765516$$
$$x_{21} = 99.9227607635738$$
$$x_{22} = 95.9593746156686$$
$$x_{23} = 109.844736107553$$
$$x_{24} = 56.7215653754984$$
$$x_{25} = 97.9406256913241$$
$$x_{26} = 60.583728892351$$
$$x_{27} = 103.889443728221$$
$$x_{28} = 115.805346154896$$
$$x_{29} = 50.9886343393585$$
$$x_{30} = 62.5237226565755$$
$$x_{31} = 64.4686693421837$$
$$x_{32} = -9.61894480741186 \cdot 10^{-5}$$
$$x_{33} = 88.0446699300268$$
$$x_{34} = 119.7815893439$$
$$x_{35} = 39.9621397880181$$
$$x_{36} = 41.7310513736826$$
$$x_{37} = 84.0947578295009$$
$$x_{38} = 91.9998011210345$$
$$x_{39} = 121.770377514453$$
$$x_{40} = 68.3711434889037$$
$$x_{41} = 58.6493938015257$$
$$x_{42} = 0$$
$$x_{43} = 43.536364764524$$
$$x_{44} = 111.831064115115$$
$$x_{45} = 70.3277433163808$$