El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$e^{5 - x} \left(2 x - 10\right) - e^{5 - x} \left(\left(x^{2} - 10 x\right) + 10\right) = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 2$$
$$x_{2} = 10$$
Solución numérica$$x_{1} = 103.683416381602$$
$$x_{2} = 117.611316367195$$
$$x_{3} = 66.1070358204964$$
$$x_{4} = 95.7367065022464$$
$$x_{5} = 62.1982992413135$$
$$x_{6} = 85.8218252058126$$
$$x_{7} = 52.5353536676441$$
$$x_{8} = 54.4505457893126$$
$$x_{9} = 77.9115782220985$$
$$x_{10} = 99.7087104090004$$
$$x_{11} = 41.5003458238026$$
$$x_{12} = 93.7518577648548$$
$$x_{13} = 101.695750825422$$
$$x_{14} = 75.9381398571095$$
$$x_{15} = 119.6026796134$$
$$x_{16} = 97.7223441832527$$
$$x_{17} = 115.620316253604$$
$$x_{18} = 50.6329315777041$$
$$x_{19} = 71.9976048399409$$
$$x_{20} = 60.2512110327951$$
$$x_{21} = 89.7848043204433$$
$$x_{22} = 64.1504791272315$$
$$x_{23} = 10$$
$$x_{24} = 48.7465984088397$$
$$x_{25} = 91.7678652853992$$
$$x_{26} = 83.8421094511834$$
$$x_{27} = 46.8810299904786$$
$$x_{28} = 58.3100990117096$$
$$x_{29} = 113.629702759959$$
$$x_{30} = 39.8482389669585$$
$$x_{31} = 56.3760726569186$$
$$x_{32} = 87.8027592857017$$
$$x_{33} = 107.660449507528$$
$$x_{34} = 73.9667334209114$$
$$x_{35} = 121.594384376032$$
$$x_{36} = 43.2435146010577$$
$$x_{37} = 111.639501452568$$
$$x_{38} = 105.67166269524$$
$$x_{39} = 109.649740213003$$
$$x_{40} = 2$$
$$x_{41} = 79.8868371329883$$
$$x_{42} = 70.0310420605412$$
$$x_{43} = 68.0673845909795$$
$$x_{44} = 81.8637338311871$$
$$x_{45} = 45.0431010802859$$