hey Jason76.
Hint: Do you know how to use calculus to find the minimum and maximum of a function in a given region?
Starting at a particle moves along the axis so that it's position at time is given by . For what values of does that particle take while moving to the left?
Answer:
Any starting hints on how this came to be? Note: This is the complete problem given.
Perhaps the answer is to simply graph the function Then you can see what values the function takes as it goes left from .
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 axis rather than the one. Yeah, I think that's the problem.
If the particle is moving to the left that means its velocity is negative. The function you were given is the position of the particle; hence the derivative of the function with respect to time gives its velocity. So take the derivative, plot that and and see where it is negative. The derivative will be a cubic function, which you should know takes a general shape of a "sideways S." It appears from the answer that t is limited to positive values only.