A particle moving on the x-axis is given by the parametric function x(t) = 2t^3 + 3t^2 - 36t

Question

If t > 0, find where (if) the particle changes direction (what (t) value) and where on the x-axis does it change direction?

Test tomorrow, please help!

Answer 1

I suggest that you graph this equation to see that it moves left for a while then moves right.

Then differentiate the function with respect to t and look for the minimum point, which is easy to find.