Derive the force for the following intervals U(x) = 1, -∞

Question

Derive the force for the following intervals
U(x) = 1, -∞ < x < -π
           |x|, -π ≤ x ≤ π
           sin (x), x > π

jamesj · Answer

$$ F = \frac{dU}{dx} \hat{x} $$
So just calculate and notice there will be points where the force is not defined because the derivative is not defined.  (Or if you know Dirac delta functions, should be written in terms of them.)

jamesj · Answer

Hence, for instance, for x < pi, the force F is the zero vector because the derivative of the potential 1 is zero.

jamesj · Answer

And I should have included a minus sign. 
$$ F = - \frac{dU}{dx} \hat{x} $$

jamesj · Answer

Making sense?

anonymous · Answer

Sorry, I don't get it :|

jamesj · Answer

What is the function U(x)?  Not its mathematical definition.  What is its physical interpretation?