El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(- \sin{\left(\frac{\sqrt{3} x}{2} \right)} - \cos{\left(\frac{\sqrt{3} x}{2} \right)}\right) e^{\frac{\left(-1\right) x}{2}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\sqrt{3} \pi}{6}$$
Solución numérica$$x_{1} = -11.7896958675224$$
$$x_{2} = -48.0656831522068$$
$$x_{3} = 89.7830685295938$$
$$x_{4} = -62.5760780660805$$
$$x_{5} = -29.9276895098646$$
$$x_{6} = 17.2310939602251$$
$$x_{7} = 53.5070812449094$$
$$x_{8} = -44.4380844237383$$
$$x_{9} = -40.8104856952699$$
$$x_{10} = -8.16209713905398$$
$$x_{11} = 49.879482516441$$
$$x_{12} = 100.665864714999$$
$$x_{13} = 42.6242850595041$$
$$x_{14} = 24.4862914171619$$
$$x_{15} = 46.2518837879726$$
$$x_{16} = -37.1828869668015$$
$$x_{17} = 86.1554698011253$$
$$x_{18} = 20.8586926886935$$
$$x_{19} = -58.9484793376121$$
$$x_{20} = 38.9966863310357$$
$$x_{21} = 57.1346799733779$$
$$x_{22} = 75.27267361572$$
$$x_{23} = 31.7414888740988$$
$$x_{24} = 68.0174761587832$$
$$x_{25} = -22.6724920529277$$
$$x_{26} = 35.3690876025672$$
$$x_{27} = 93.4106672580622$$
$$x_{28} = 6.34829777481976$$
$$x_{29} = 28.1138901456304$$
$$x_{30} = -33.555288238333$$
$$x_{31} = -55.3208806091436$$
$$x_{32} = 13.6034952317566$$
$$x_{33} = -26.3000907813962$$
$$x_{34} = -15.4172945959909$$
$$x_{35} = 71.6450748872516$$
$$x_{36} = 64.3898774303147$$
$$x_{37} = -0.906899682117109$$
$$x_{38} = 2.72069904635133$$
$$x_{39} = 82.5278710726569$$
$$x_{40} = 60.7622787018463$$
$$x_{41} = 9.9758965032882$$
$$x_{42} = -4.53449841058554$$
$$x_{43} = 97.0382659865307$$
$$x_{44} = 78.9002723441885$$
$$x_{45} = -19.0448933244593$$
$$x_{46} = -51.6932818806752$$
$$x_{47} = 158.707444370494$$