The potential energy U(x) of a particle moving along x - axis is given by `U(x)=ax-bx^(2)`. Find the equilibrium position of particle.

Explanation

To find the equilibrium position of a particle moving along the x-axis with a given potential energy function \( U(x) = ax - bx^2 \), we can follow these steps:

### Step 1: Understand the condition for equilibrium
At equilibrium, the net force acting on the particle is zero. The force \( F \) can be derived from the potential energy \( U(x) \) using the relationship:
\[ F = -\frac{dU}{dx} \]
Setting the force to zero gives us the condition for equilibrium:
...