El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin{\left(\frac{\sqrt{7} x}{2} \right)} + \cos{\left(\frac{\sqrt{7} x}{2} \right)}\right) e^{\frac{3 x}{2}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\sqrt{7} \pi}{14}$$
Solución numérica$$x_{1} = -24.3419134403364$$
$$x_{2} = -17.217450969994$$
$$x_{3} = -0.593705205861863$$
$$x_{4} = -31.4663759106787$$
$$x_{5} = -95.5865381437599$$
$$x_{6} = -90.836896496865$$
$$x_{7} = -57.5894049686007$$
$$x_{8} = -78.9627923796278$$
$$x_{9} = -74.2131507327329$$
$$x_{10} = -48.0901216748109$$
$$x_{11} = 1.78111561758559$$
$$x_{12} = 16.0300405582703$$
$$x_{13} = -5.34334685275677$$
$$x_{14} = -59.9642257920482$$
$$x_{15} = -7.71816767620422$$
$$x_{16} = -36.2160175575736$$
$$x_{17} = -14.8426301465466$$
$$x_{18} = -33.8411967341262$$
$$x_{19} = -71.8383299092854$$
$$x_{20} = -83.7124340265227$$
$$x_{21} = -45.7153008513635$$
$$x_{22} = -50.4649424982584$$
$$x_{23} = -29.0915550872313$$
$$x_{24} = -10.0929884996517$$
$$x_{25} = -67.0886882623905$$
$$x_{26} = -2.96852602930931$$
$$x_{27} = -52.8397633217058$$
$$x_{28} = -76.5879715561803$$
$$x_{29} = 4.15593644103304$$
$$x_{30} = 8.90557808792794$$
$$x_{31} = -100.336179790655$$
$$x_{32} = -69.463509085838$$
$$x_{33} = 13.6552197348228$$
$$x_{34} = -62.3390466154956$$
$$x_{35} = -38.5908383810211$$
$$x_{36} = -26.7167342637838$$
$$x_{37} = -12.4678093230991$$
$$x_{38} = -64.7138674389431$$
$$x_{39} = -40.9656592044685$$
$$x_{40} = -55.2145841451533$$
$$x_{41} = -88.4620756734176$$
$$x_{42} = -81.3376132030752$$
$$x_{43} = -21.9670926168889$$
$$x_{44} = -43.340480027916$$
$$x_{45} = -97.9613589672074$$
$$x_{46} = 6.53075726448049$$
$$x_{47} = -19.5922717934415$$
$$x_{48} = -86.0872548499701$$
$$x_{49} = 18.4048613817178$$
$$x_{50} = 20.7796822051652$$
$$x_{51} = 11.2803989113754$$
$$x_{52} = -93.2117173203125$$