Starting at $\displaystyle t = 0$ a particle moves along the $\displaystyle x$ axis so that it's position at time $\displaystyle t$ is given by $\displaystyle x(t) = t^{4} - 5t^{2} + 2t$. For what values of $\displaystyle t$ does that particle take while moving to the left?

Answer: $\displaystyle 0.203 < t < 1.470$

Any starting hints on how this came to be? Note: This is the complete problem given.

Perhaps the answer is tosimply graph the functionThen you can see what values the function takes as it goes left from $\displaystyle 0$.

But the problem is that a graph goes on forever to the left. So how can there be a left interval?

But perhaps this is some kind of flipped graph, where time is on the $\displaystyle y$ axis rather than the $\displaystyle x$ one. Yeah, I think that's the problem.