Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$- 2 \left(2 x^{2} \cos{\left(x^{2} + 1 \right)} + \sin{\left(x^{2} + 1 \right)}\right) = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 43.9619214434102$$
$$x_{2} = -75.4945028307817$$
$$x_{3} = -89.8405386523628$$
$$x_{4} = 9.73775378723$$
$$x_{5} = 10.6617320557088$$
$$x_{6} = 89.6830421633998$$
$$x_{7} = 5.65706155582907$$
$$x_{8} = 24.2497313967903$$
$$x_{9} = 25.5123743271578$$
$$x_{10} = 70.1672757491473$$
$$x_{11} = -56.9446623400667$$
$$x_{12} = -43.8545979379999$$
$$x_{13} = -76.2604673739696$$
$$x_{14} = 20.0672842611393$$
$$x_{15} = -1.01229453086059$$
$$x_{16} = 2.63173856168775$$
$$x_{17} = 98.5774666205898$$
$$x_{18} = 56.0269757933469$$
$$x_{19} = -33.8247093003621$$
$$x_{20} = 46.1581070900829$$
$$x_{21} = -41.8757660486458$$
$$x_{22} = 13.5198337885067$$
$$x_{23} = 80.0196019886973$$
$$x_{24} = 56.6404188852419$$
$$x_{25} = 1.01229453086059$$
$$x_{26} = 51.0387235155318$$
$$x_{27} = -57.8749402965492$$
$$x_{28} = 97.2458983016984$$
$$x_{29} = 18.2642031441833$$
$$x_{30} = -29.8794857718858$$
$$x_{31} = -45.679191739084$$
$$x_{32} = -91.8805219605876$$
$$x_{33} = 9.06963525509434$$
$$x_{34} = -7.76333386150031$$
$$x_{35} = 6.1873231744953$$
$$x_{36} = -48.3844761967088$$
$$x_{37} = 79.2305054751583$$
$$x_{38} = -21.8653590295624$$
$$x_{39} = -4.03849070189123$$
$$x_{40} = -50.6680588642432$$
$$x_{41} = -15.8713639465704$$
$$x_{42} = 1.96005320703295$$
$$x_{43} = 49.823982117835$$
$$x_{44} = -13.7502363642665$$
$$x_{45} = 42.2492095035932$$
$$x_{46} = -93.8929168735086$$
$$x_{47} = 86.0358248390295$$
$$x_{48} = -26.3006065129735$$
$$x_{49} = -27.7535879768054$$
$$x_{50} = 28.3693344458994$$
$$x_{51} = -9.73775378723$$
$$x_{52} = -54.6933923768852$$
$$x_{53} = -31.8145269456219$$
$$x_{54} = -75.6192403644685$$
$$x_{55} = 13.6355217026362$$
$$x_{56} = 64.0584961091231$$
$$x_{57} = -19.7516978256737$$
$$x_{58} = 3.16943334466592$$
$$x_{59} = -99.765406695581$$
$$x_{60} = -59.639364691151$$
$$x_{61} = 6.67565073578945$$
$$x_{62} = -37.3555657543961$$
$$x_{63} = 4.03849070189123$$
$$x_{64} = -51.1923750202349$$
$$x_{65} = 36.6765977670048$$
$$x_{66} = -86.0540803701783$$
$$x_{67} = -71.3438924742338$$
$$x_{68} = -69.8531623466111$$
$$x_{69} = -81.7864391605895$$
$$x_{70} = 66.4181224916093$$
$$x_{71} = 51.6809901131857$$
$$x_{72} = 21.3565640340599$$
$$x_{73} = -83.9099517580327$$
$$x_{74} = -11.7815311084128$$
$$x_{75} = -6.67565073578945$$
$$x_{76} = -37.8982715587281$$
$$x_{77} = 100.001301305042$$
$$x_{78} = -3.16943334466592$$
$$x_{79} = 106.6890857783$$
$$x_{80} = 3.62975193593284$$
$$x_{81} = -71.9577347198112$$
$$x_{82} = 82.2460932410883$$
$$x_{83} = 8.15792589208374$$
$$x_{84} = 58.1727275619276$$
$$x_{85} = 71.9359019781622$$
$$x_{86} = 94.0934585963188$$
$$x_{87} = 47.3342009703147$$
$$x_{88} = 32.1582845133909$$
$$x_{89} = -1.96005320703295$$
$$x_{90} = -18.3500053177433$$
$$x_{91} = 20.2232307965203$$
$$x_{92} = 8.53430091745704$$
Сonvexity and concavity intervals:Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left[97.2458983016984, \infty\right)$$
Convex at the intervals
$$\left(-\infty, -91.8805219605876\right]$$