El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$e^{5 x} x = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
Solución numérica$$x_{1} = -40.097339700484$$
$$x_{2} = -28.1077377499122$$
$$x_{3} = -72.0871417253055$$
$$x_{4} = -100.083702520396$$
$$x_{5} = -62.0891526430468$$
$$x_{6} = -22.1177220793576$$
$$x_{7} = -76.0864902902439$$
$$x_{8} = -50.0926804134861$$
$$x_{9} = -104.083365880228$$
$$x_{10} = -38.0985856557447$$
$$x_{11} = -94.0842625773975$$
$$x_{12} = -26.1105003061778$$
$$x_{13} = -46.0942876944303$$
$$x_{14} = -8.22763502772369$$
$$x_{15} = -64.0886982550436$$
$$x_{16} = -12.1624810640769$$
$$x_{17} = -102.08353082211$$
$$x_{18} = -96.0840679178704$$
$$x_{19} = -24.1137757759865$$
$$x_{20} = -98.083881398955$$
$$x_{21} = -88.0849011032851$$
$$x_{22} = 0$$
$$x_{23} = -54.0913222520768$$
$$x_{24} = -30.1053762154051$$
$$x_{25} = -16.1365788145515$$
$$x_{26} = -14.1472558033337$$
$$x_{27} = -34.1015508687036$$
$$x_{28} = -90.0846785476673$$
$$x_{29} = -6.32493857675712$$
$$x_{30} = -18.1286686167371$$
$$x_{31} = -74.0868069143416$$
$$x_{32} = -36.0999799755566$$
$$x_{33} = -66.0882724311596$$
$$x_{34} = -84.0853789252274$$
$$x_{35} = -44.0952072175632$$
$$x_{36} = -48.0934488158397$$
$$x_{37} = -58.0901594387814$$
$$x_{38} = -60.089638569989$$
$$x_{39} = -82.0856358346555$$
$$x_{40} = -68.0878725593843$$
$$x_{41} = -78.0861904100623$$
$$x_{42} = -42.0962196099167$$
$$x_{43} = -56.0907191603359$$
$$x_{44} = -52.0919739603108$$
$$x_{45} = -70.0874963368298$$
$$x_{46} = -32.103334188641$$
$$x_{47} = -86.0851343017212$$
$$x_{48} = -20.1225696413239$$
$$x_{49} = -92.084465922444$$
$$x_{50} = -80.0859059795857$$
$$x_{51} = -10.186023560538$$