Kinematics (Complex)

Quote:

Originally Posted by Air

Question:
A particle moves on the positive x-axis. The particle is moving towards the origin $O$ when it passes through the point $A$ , where $x=2a$ , with speed $\sqrt{\left(\frac{k}{a}\right)}$ , where $k$ is constant. Given that the particle experiences an acceleration $\frac{k}{2x^2} + \frac{k}{4a^2}$ in a direction away from $O$ , show that it come instantaneously to rest at a point $B$ , where $x=a$ . Immediately the particle reaches B the acceleration changes to $\frac{k}{2x^2} - \frac{k}{4a^2}$ in a direction away from $O$ . Show that the particle next comes instantaneously to rest at $A$ .

My Problem with this question:
I have no idea on how to approach it. Please help. Thanks in advance.

HAve you tried taking the derivative and realizing that there is a max or min when v(t)=0?