Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{x} x^{6} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = -78.9671108208535$$
$$x_{2} = -58.162685619902$$
$$x_{3} = -110.24134484425$$
$$x_{4} = 0$$
$$x_{5} = -96.4861171978203$$
$$x_{6} = -71.2864585440044$$
$$x_{7} = -106.303377433517$$
$$x_{8} = -56.3423143698061$$
$$x_{9} = -120.107453884621$$
$$x_{10} = -100.40770624888$$
$$x_{11} = -116.15774602451$$
$$x_{12} = -82.8370640708798$$
$$x_{13} = -114.184456627505$$
$$x_{14} = -77.0387854017141$$
$$x_{15} = -67.4854672597338$$
$$x_{16} = -108.27167551581$$
$$x_{17} = -54.5425970346382$$
$$x_{18} = -60.0006716761699$$
$$x_{19} = -65.5977440883992$$
$$x_{20} = -75.1155185220878$$
$$x_{21} = -73.1978637909425$$
$$x_{22} = -92.5729433217803$$
$$x_{23} = -112.21229846825$$
$$x_{24} = -118.132099183578$$
$$x_{25} = -61.8538036962972$$
$$x_{26} = -51.0212656989008$$
$$x_{27} = -84.7778953156122$$
$$x_{28} = -94.5283960776019$$
$$x_{29} = -86.7221756752623$$
$$x_{30} = -80.9000115859487$$
$$x_{31} = -122.083752661696$$
$$x_{32} = -104.336545566176$$
$$x_{33} = -90.6199460984893$$
$$x_{34} = -63.7200546034686$$
$$x_{35} = -102.371283845722$$
$$x_{36} = -88.6696127131053$$
$$x_{37} = -52.7673199737009$$
$$x_{38} = -98.4459380391843$$
$$x_{39} = -69.382040298942$$