What is the relationship between force and potential energy?

[ChloeYip]

Homework Statement

Picture: https://drive.google.com/open?id=0B39n6QfDU8f3bWY3OWxyaGZBYU0

[Moderator: Image inserted to make problem statement visible]

Homework Equations

F=-dU/dx

The Attempt at a Solution

I have no idea in this question...
The slope is always the same for the graph...
Also, i have no idea how to link the graph to the equation...

Thanks.

 

[haruspex]

F=-dU/dx

Equations have context, and are meaningless without it. In that equation, what, precisely, do all the variables represent?
Here's another equation: $W=\int_{\vec a}^{\vec b}\vec F.\vec {dx}$, where W is the work done by a force $\vec F$, a function of $\vec x$, that moves from $\vec x=\vec a$ to $\vec x=\vec b$.
See if you can apply that as x moves a little to the right and left of point a.