Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$x e^{\frac{\left(-1\right) x^{2}}{2}} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = 9.02289694337605$$
$$x_{2} = 66.5562459808845$$
$$x_{3} = -40.4883834667848$$
$$x_{4} = 78.5094259967043$$
$$x_{5} = -28.6943596043799$$
$$x_{6} = -20.9648808652053$$
$$x_{7} = -86.228064985273$$
$$x_{8} = -94.2086933283192$$
$$x_{9} = -84.2334824940775$$
$$x_{10} = -60.3265078154327$$
$$x_{11} = -76.2579924560991$$
$$x_{12} = -74.2649444149412$$
$$x_{13} = -30.6488081209205$$
$$x_{14} = 94.4654798903143$$
$$x_{15} = 27.0151495573047$$
$$x_{16} = -62.3160212977879$$
$$x_{17} = 13.8305646213614$$
$$x_{18} = -72.2722807950237$$
$$x_{19} = -96.2043534607085$$
$$x_{20} = -68.2882415884721$$
$$x_{21} = 19.3379596244699$$
$$x_{22} = -90.2179499984874$$
$$x_{23} = 74.5233591950223$$
$$x_{24} = 90.4750104191475$$
$$x_{25} = 100.45260622169$$
$$x_{26} = 15.6247818795334$$
$$x_{27} = -50.3914159606663$$
$$x_{28} = 92.4701421572582$$
$$x_{29} = -70.2800343339193$$
$$x_{30} = 46.6877762829739$$
$$x_{31} = 62.5758396530863$$
$$x_{32} = -19.0686408223086$$
$$x_{33} = 98.4567232107033$$
$$x_{34} = -88.2228929179074$$
$$x_{35} = 72.5309015703522$$
$$x_{36} = -82.2391633180928$$
$$x_{37} = -100.196193168581$$
$$x_{38} = 38.7783713446935$$
$$x_{39} = -48.4076116917235$$
$$x_{40} = 25.0766626196802$$
$$x_{41} = 58.5981051512238$$
$$x_{42} = 60.5866054706585$$
$$x_{43} = -56.3497113142373$$
$$x_{44} = -78.2513955147154$$
$$x_{45} = 28.9620890166341$$
$$x_{46} = -32.6088462722306$$
$$x_{47} = -46.4252005910588$$
$$x_{48} = 64.5657397621909$$
$$x_{49} = -8.82065718477295$$
$$x_{50} = 17.465102009593$$
$$x_{51} = 42.7288452402976$$
$$x_{52} = 7.83657923190551$$
$$x_{53} = 12.1040591364533$$
$$x_{54} = 23.1487959086869$$
$$x_{55} = -17.1969684851483$$
$$x_{56} = -54.362591820007$$
$$x_{57} = 48.6697660202548$$
$$x_{58} = 30.9158612891769$$
$$x_{59} = 84.4909972102885$$
$$x_{60} = -52.3764545425553$$
$$x_{61} = -34.5735053916839$$
$$x_{62} = 76.5162106782208$$
$$x_{63} = 32.8752332341382$$
$$x_{64} = 54.623627287895$$
$$x_{65} = -58.3377124249816$$
$$x_{66} = -80.2451271074651$$
$$x_{67} = -36.5420283825472$$
$$x_{68} = 96.4610108264976$$
$$x_{69} = 21.2345123835376$$
$$x_{70} = 44.7073945322353$$
$$x_{71} = -7.6886044567655$$
$$x_{72} = 52.6378406446428$$
$$x_{73} = -38.5138150497611$$
$$x_{74} = 56.6104161729572$$
$$x_{75} = -15.3593372555059$$
$$x_{76} = 34.8392502079753$$
$$x_{77} = 82.4968425477036$$
$$x_{78} = -10.247960314217$$
$$x_{79} = 88.4800986212492$$
$$x_{80} = -11.8535751456397$$
$$x_{81} = 68.5473054354995$$
$$x_{82} = 10.4810551180426$$
$$x_{83} = 36.8071620516744$$
$$x_{84} = -66.2969435075443$$
$$x_{85} = 0$$
$$x_{86} = -22.8793491121891$$
$$x_{87} = 80.5029780991381$$
$$x_{88} = -42.4653421912683$$
$$x_{89} = 50.6531744084895$$
$$x_{90} = -98.2001902620909$$
$$x_{91} = 70.5388712182941$$
$$x_{92} = -64.3061861108853$$
$$x_{93} = -13.5703851876112$$
$$x_{94} = -26.7467597908737$$
$$x_{95} = -24.8076741592432$$
$$x_{96} = -92.2132213430942$$
$$x_{97} = -44.4443699549213$$
$$x_{98} = 40.7523965392307$$
$$x_{99} = 86.4854219951314$$