Potential energy particle problem

[Hiche]

Homework Statement

A single conservative force F = (4.0x - 13)i N, where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 26 J at x = 0. (a) What is the maximum positive potential energy? At what (b) negative value and (c) positive value of x is the potential energy equal to zero?

Homework Equations

Force = dU/dx where U is the potential energy.

The Attempt at a Solution

Okay, so we find the anti-derivative of the given force then we have: U = x^2/2 - 13x. Then what? At x = 0 m, U is 26 J. At the maximum U, we know the kinetic energy is 0 (v = 0).

 

[Simon Bridge]

note:
force is zero when x=13/4, everywhere else it points away from there.

the indefinite integral of 4x-13 is actually

2x²-13x+c

Which is a quadratic (c is the constant of integration).

The turning point, is where the derivative is equal to zero :) though, in this case, it looks like a minima rather than the asked-for maxima (check the equation does not have a minus sign in front).