In general, I want to know if it is possible to know if an extremum exists for the derivative of a function just by looking at the graph of the function.
As a specific problem, I want to be able to predict that there will be a maximum possible force caused by Lennard-Jones potential.
Lennard-Jones potential is $y=x^{-12}-x^{-6}$ shown in orange, and the negative of its derivative (force due to this potential), $y'=12 x^{-13}-6 x^{-7}$ is in blue.
