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 derivative−x2log(x)1+log(x)1=0Solve this equationThe roots of this equation
x1=e−1Сonvexity 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
(−∞,e−1]Convex at the intervals
[e−1,∞)