The force F acting on a body moving along x-axis varies with the position x of the particle as shown in the graph. The body is in stable equilibrium at 

 

$\begin{array}{l}\text{If }\frac{d^{2}U}{d{x}^2}>0,\text{\hspace{0.17em}then it is the position of stable equillibrium}\\ \text{If }\frac{d^{2}U}{d{x}^2}<0,\text{\hspace{0.17em}then it is the position of unstable equillibrium}\\ {\text{At x}}_1,\frac{dF}{dx}>0\Rightarrow \frac{d}{dx}\left(-\frac{dU}{dx}\right)>0,\text{ i.e., }\frac{d^{2}U}{d{x}^2}<0\\ {\text{x}}_1\text{\hspace{0.17em}is the position of unstable equillibrium}\\ {\text{At x}}_2,\frac{dF}{dx}<0\Rightarrow \frac{d}{dx}\left(-\frac{dU}{dx}\right)<0,\text{ i.e., }\frac{d^{2}U}{d{x}^2}>0\\ {\text{x}}_2\text{\hspace{0.17em}is the position of stable equillibrium}\end{array}$