Particle's acceleration when it achieves maximum displacement in the +x direction

Question

I'm not sure if this goes in the physics section or the mathematics section, but this question seems pretty math oriented, so I'll ask it here.

$t\ge0$ and $v_x=24-3t^3$

I have to find the particle's acceleration when it achieves maximum displacement in the $+x$ direction. I'm not sure how to know exactly when the particle hits maximum displacement.

Answer 1

HINT:

Maximum displacement occurs at the time when the velocity reaches zero. (Why? You can think either from a physical perspective or a mathematical one.)

And acceleration is the derivative of the velocity with respect to time.

Can you proceed now?