Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada$$2 \left(- x^{2} \cos{\left(x \right)} - 4 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$x_{1} = -92.7201071560939$$
$$x_{2} = -83.3002013673394$$
$$x_{3} = 80.1604867055981$$
$$x_{4} = -80.1604867055981$$
$$x_{5} = -23.7295255625192$$
$$x_{6} = -70.7423403203845$$
$$x_{7} = -33.1071774728736$$
$$x_{8} = 99.0005586689926$$
$$x_{9} = -45.6405949760108$$
$$x_{10} = 67.6033676125647$$
$$x_{11} = -17.5048370447411$$
$$x_{12} = -8.31398471094493$$
$$x_{13} = -29.978069966608$$
$$x_{14} = -64.4646492226716$$
$$x_{15} = -26.8518211351302$$
$$x_{16} = -86.4400521937386$$
$$x_{17} = 55.0504523208123$$
$$x_{18} = -5.38572965402801$$
$$x_{19} = 2.68896749918069$$
$$x_{20} = 83.3002013673394$$
$$x_{21} = -36.2384169134664$$
$$x_{22} = 58.1881390858586$$
$$x_{23} = 48.7765781423002$$
$$x_{24} = 33.1071774728736$$
$$x_{25} = -2.68896749918069$$
$$x_{26} = 11.3396400694003$$
$$x_{27} = 95.86028820339$$
$$x_{28} = -73.8815350660339$$
$$x_{29} = 0.599741421027824$$
$$x_{30} = -77.0209248041715$$
$$x_{31} = -67.6033676125647$$
$$x_{32} = 20.6129075025746$$
$$x_{33} = 36.2384169134664$$
$$x_{34} = 86.4400521937386$$
$$x_{35} = 92.7201071560939$$
$$x_{36} = -11.3396400694003$$
$$x_{37} = 61.3262239938688$$
$$x_{38} = 73.8815350660339$$
$$x_{39} = -58.1881390858586$$
$$x_{40} = -14.4104316197583$$
$$x_{41} = -95.86028820339$$
$$x_{42} = 29.978069966608$$
$$x_{43} = -99.0005586689926$$
$$x_{44} = 77.0209248041715$$
$$x_{45} = 45.6405949760108$$
$$x_{46} = -20.6129075025746$$
$$x_{47} = 89.5800249069094$$
$$x_{48} = -51.9132353685519$$
$$x_{49} = -42.5054334829582$$
$$x_{50} = 51.9132353685519$$
$$x_{51} = -55.0504523208123$$
$$x_{52} = 64.4646492226716$$
$$x_{53} = 5.38572965402801$$
$$x_{54} = -39.3712875521166$$
$$x_{55} = -61.3262239938688$$
$$x_{56} = 26.8518211351302$$
$$x_{57} = -0.599741421027824$$
$$x_{58} = 14.4104316197583$$
$$x_{59} = 42.5054334829582$$
$$x_{60} = 70.7423403203845$$
$$x_{61} = -48.7765781423002$$
$$x_{62} = 17.5048370447411$$
$$x_{63} = 8.31398471094493$$
$$x_{64} = 39.3712875521166$$
$$x_{65} = 23.7295255625192$$
$$x_{66} = -89.5800249069094$$
Intervalos de convexidad y concavidad:Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
$$\left[95.86028820339, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -99.0005586689926\right]$$