about energy?

Question

the potential energy of an object is given by U(x)= 3x^2-2x^3, where U is in joules and x is in meters.
a. determine the force acting on this object.
b. at what positions is this object in equilibrium/
c. which of this equilibrium positions are stable and which are unstable?

Answer 1

a)By definition force F=dU/dx
So by differentiating we have
F= 6x - 6x^2

b) F=0 at equilibrium
F= 6x - 6x^2=0 possible solutions are
x1 = 0 m
x2= 1m

c) Should I do this one too? (hint: if there is no potential energy there is no potential for work to be done. Is it? That seems stable to me)