How Do We Determine the Minimum of a Potential Function in Physics?

[Shafikae]

If we have a particle of mass m moving in the presence of the following potential in one dimension:

V(x) = V₀ [(e^{-2$$\gamma$$x}) - 2e^-$$\gamma$$x)]

In order to find the minimum of the potential V do we take the derivative with respect to x?



dV(x)/dx = 2*$$\gamma$$V₀[(e^-$$\gamma$$x) - (e^{-2$$\gamma$$x})]


Is this how we find the minimum potential of V?

And how do we sketch a graph of V?

 

[Office_Shredder]

A point can only be a minimum of a function if the derivative at that point equals what?

 

[Shafikae]

zero?