Question 1142313
<br>
{{{graph(400,400,-1,4,-15,5,x^3-12x+3)}}}<br>
The graph of the function between t=0 and t=3 shows that the function value is 3 and decreasing at t=0, and -6 and increasing at t=3.<br>
That means there is a local minimum between t=0 and t=3.<br>
Calculus shows that minimum (where the derivative is zero) is -13, at t=2. (Or you can use a graphing calculator to find the minimum.)<br>
So the particle travels from 3 to -13 and then from -13 to -6.  That gives one of the given answer choices.