First you need to determine the acceleration by taking the second derivative of x(t), a(t) = d²x(t)/dt²
Next, take the first derivative of a(t). Find the extreme points by setting da(t)/dt = 0 and solving for t.
To determine if each extreme point is a maximum or minimum, take the second derivative of a(t) and plug in the t values of the extreme points. If a"(t) is positive, then the point is a minimum. If a"(t) is negative, then a"(t) is a maximum