Final answer:
The biggest force in the negative x direction occurs where the potential energy function has the steepest upward slope when moving away from zero, as force is the negative gradient of potential energy (F = -dU/dx).
Step-by-step explanation:
The question asks where the force is the biggest in the negative x direction based on a potential energy function U as a function of x. In physics, the force experienced by an object is related to the potential energy through the negative derivative of the potential energy with respect to displacement. That is, F = -dU/dx.
The greatest force in the negative x direction will occur where this derivative is most positive (since the force is negative of the derivative). In a graph of U versus x, this is at a point where we have the steepest upward slope. Essentially, for a one-dimensional motion, this gives the complete vector force in the x-direction.
Using the given equation for potential energy, and looking at its slope - which is how we derive the force - we can determine that the biggest force in the negative x direction occurs at the point where the potential energy function is most steeply increasing as x moves away from zero.