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$$x_{1} = -81.8167544117873$$
$$x_{2} = -43.254793289805$$
$$x_{3} = -77.8771426363418$$
$$x_{4} = -54.5046825561654$$
$$x_{5} = -105.566581155148$$
$$x_{6} = -62.2229958168436$$
$$x_{7} = -119.473696806211$$
$$x_{8} = -71.9837938598591$$
$$x_{9} = -103.58224722089$$
$$x_{10} = -85.7632268036374$$
$$x_{11} = -48.8085971699827$$
$$x_{12} = -56.4237044386907$$
$$x_{13} = -68.068485074228$$
$$x_{14} = -39.6921638743108$$
$$x_{15} = -60.2838279161017$$
$$x_{16} = -87.7386796067909$$
$$x_{17} = -101.598637273947$$
$$x_{18} = 0$$
$$x_{19} = -115.49759696096$$
$$x_{20} = -6.37672685750786 \cdot 10^{-5}$$
$$x_{21} = -89.7154509915966$$
$$x_{22} = -79.846010822632$$
$$x_{23} = -73.9458061467892$$
$$x_{24} = -91.6934372760935$$
$$x_{25} = -113.510274213085$$
$$x_{26} = -97.6338001722932$$
$$x_{27} = -83.7892084427348$$
$$x_{28} = -66.1158854871866$$
$$x_{29} = -52.5946760133184$$
$$x_{30} = -99.615802770923$$
$$x_{31} = -117.485413951559$$
$$x_{32} = -95.6526915671241$$
$$x_{33} = -50.6953021085607$$
$$x_{34} = -109.537236988787$$
$$x_{35} = -93.6725453940216$$
$$x_{36} = -121.46241928026$$
$$x_{37} = -111.523476442329$$
$$x_{38} = -41.454503250211$$
$$x_{39} = -70.0245793288288$$
$$x_{40} = -107.551592080799$$
$$x_{41} = -58.3504397456909$$
$$x_{42} = -45.0843950117395$$
$$x_{43} = -75.9103368174603$$
$$x_{44} = -64.1672177737049$$
$$x_{45} = -46.9371649842841$$