Let's find the inflection points, we'll need to solve the equation for this
dx2d2f(x)=0(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
dx2d2f(x)=the second derivative6x=0Solve this equationThe roots of this equation
x1=0Сonvexity 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
[0,∞)Convex at the intervals
(−∞,0]