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$$2 \left(- \sin{\left(x \right)} \cosh{\left(x \right)} + \cos{\left(x \right)} \sinh{\left(x \right)}\right) = 0$$
Solve this equationThe roots of this equation
$$x_{1} = -29.0597320457056$$
$$x_{2} = -13.3517687777541$$
$$x_{3} = 16.4933614313464$$
$$x_{4} = 19.6349540849362$$
$$x_{5} = 29.0597320457056$$
$$x_{6} = -7.06858274562873$$
$$x_{7} = -16.4933614313464$$
$$x_{8} = 7.06858274562873$$
$$x_{9} = 3.92660231204792$$
$$x_{10} = 22.776546738526$$
$$x_{11} = -3.92660231204792$$
$$x_{12} = -10.210176122813$$
$$x_{13} = 10.210176122813$$
$$x_{14} = 25.9181393921158$$
$$x_{15} = 13.3517687777541$$
$$x_{16} = -25.9181393921158$$
$$x_{17} = -22.776546738526$$
$$x_{18} = 0$$
$$x_{19} = -19.6349540849362$$
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
$$\left[29.0597320457056, \infty\right)$$
Convex at the intervals
$$\left(-\infty, -29.0597320457056\right]$$