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$$2 \left(- \left(\cosh^{2}{\left(x + 1 \right)} + 1\right) \left(\tanh^{2}{\left(x + 1 \right)} - 1\right)^{2} - 2 \left(\cosh^{2}{\left(x + 1 \right)} + 1\right) \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \tanh^{2}{\left(x + 1 \right)} - \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \sinh^{2}{\left(x + 1 \right)} + 4 \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \sinh{\left(x + 1 \right)} \cosh{\left(x + 1 \right)} \tanh{\left(x + 1 \right)} - \left(\tanh^{2}{\left(x + 1 \right)} - 1\right) \cosh^{2}{\left(x + 1 \right)} + \sin^{2}{\left(x + 1 \right)} - \cos^{2}{\left(x + 1 \right)} + 1\right) = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 42.9822972067506$$
$$x_{2} = -16.7079631948138$$
$$x_{3} = 20.9911483264984$$
$$x_{4} = -70.1150382894341$$
$$x_{5} = 30.4159264394344$$
$$x_{6} = 17.8495558674774$$
$$x_{7} = 39.8407046101773$$
$$x_{8} = 64.9734457627567$$
$$x_{9} = -66.9734459700171$$
$$x_{10} = -51.2654826753886$$
$$x_{11} = -48.1238897092746$$
$$x_{12} = 17.8495560299547$$
$$x_{13} = 49.2654823964173$$
$$x_{14} = 71.2566312860504$$
$$x_{15} = -82.6814087363722$$
$$x_{16} = -82.681408910892$$
$$x_{17} = 58.690260212759$$
$$x_{18} = 83.8230017693038$$
$$x_{19} = 99.5309651439364$$
$$x_{20} = 24.1327414061396$$
$$x_{21} = -1.45129545590714$$
$$x_{22} = 55.5486679892229$$
$$x_{23} = -22.9911488221202$$
$$x_{24} = -60.6902601613349$$
$$x_{25} = -88.9645945436711$$
$$x_{26} = -22.9911484706459$$
$$x_{27} = -16.7079631423494$$
$$x_{28} = 86.9645943169109$$
$$x_{29} = 52.4070750189247$$
$$x_{30} = 93.247779860089$$
$$x_{31} = -29.2743340978911$$
$$x_{32} = -19.8495557985803$$
$$x_{33} = 49.265482350792$$
$$x_{34} = 86.964594718588$$
$$x_{35} = -29.2743339463623$$
$$x_{36} = -57.5486678779633$$
$$x_{37} = -79.5398164571782$$
$$x_{38} = -35.5575192986956$$
$$x_{39} = 49.2654827118511$$
$$x_{40} = -60.6902603656641$$
$$x_{41} = 27.2743338399742$$
$$x_{42} = 14.707963225495$$
$$x_{43} = -76.3982234765515$$
$$x_{44} = 80.6814087905806$$
$$x_{45} = 27.2743341374979$$
$$x_{46} = -92.1061868697346$$
$$x_{47} = 74.3982235984748$$
$$x_{48} = -63.8318529852173$$
$$x_{49} = 20.9911486490739$$
$$x_{50} = -98.3893720544106$$
$$x_{51} = 71.2566309544896$$
$$x_{52} = 96.389372178087$$
$$x_{53} = -120.380521214309$$
$$x_{54} = -88.964594159178$$
$$x_{55} = 93.2477795140332$$
$$x_{56} = 42.9822969010573$$
$$x_{57} = 77.5398165666147$$
$$x_{58} = -95.2477798301763$$
$$x_{59} = -26.1327411292434$$
$$x_{60} = -44.9822973961636$$
$$x_{61} = -54.407074898757$$
$$x_{62} = -85.8230015743177$$
$$x_{63} = 68.1150387632651$$
$$x_{64} = 61.8318531897853$$
$$x_{65} = 36.6991116349999$$
$$x_{66} = 86.9645940506399$$
$$x_{67} = -73.2566312528174$$
$$x_{68} = 64.9734454757735$$
$$x_{69} = -38.699111817712$$
$$x_{70} = -95.2477796535486$$
$$x_{71} = -44.9822970324124$$
$$x_{72} = 33.5575194117619$$
$$x_{73} = -0.548704544092859$$
$$x_{74} = -41.8407043935162$$
$$x_{75} = -32.4159263210277$$
$$x_{76} = -66.9734455952915$$
$$x_{77} = -51.2654821047327$$
$$x_{78} = -38.6991115864245$$
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
$$\left[14.707963225495, \infty\right)$$
Convex at the intervals
$$\left[-1.45129545590714, -0.548704544092859\right]$$