The potential energy of particle is u (x ,y , z) = e^-(x + y + z). find the force acting on the particle. show that the force is conservative. a particle of mass m constrained to move along the positive x-axis under the influence of a conservative force has a potential energy u(x) = a/x^4 - b/x^2 , 0 < a < b find any potential energy maxima and/ or minima, examine the behavior of u as x approaches 0 and infinity, and sketch both the potential energy of the particle and force acting on the particle vs position on the same plot. if the total energy of the particle is zero, are there any turning points? if so, find it/them. is the particle bounded? if the particle starts at rest at t = 0, find the position of the particle at any time t. part c is a tedious, but "doable" problem. use an on-line integrator to do the integration starting with equation 4.58 and aggregate terms so you don't have to carry them all throughout the equations.