1. The problem statement, all variables and given/known data A particle can only move along the x axis. Forces act on it so that its potential energy function is U(x) = 1/2*k1*x^2 + 1/4*k2*x^4 where k1 and k2 are positive. The particle is started at x = a with zero velocity. a.) Where is the velocity a maximum? What is its magnitude? b.) Where else will the velocity be zero? c.) What is the force on the particle as a function of x? 2. Relevant equations F = d/dx -U(x) W = -U(x2) + U(x1) 3. The attempt at a solution It's asking for the point where the velocity is maximum so the acceleration has to equal zero or not exist. The function exists at all x-values so we need to find the acceleration as a function of x. since F = d/dx -U(x), F = -(k1*x + k2*x^3) F = ma ma = -(k1*x + k2*x^3) a = -1/m*(k1*x + k2*x^3) When a = 0 0 = -1/m*(k1*x + k2*x^3) -k1*x = k2*x^3 x^2 = -k1/k2 x = sqrt(-k1/k2) I'm completely lost at this point. Thanks for the help!