Applications of Derivatives Questions

[xmen]

Edited

 

[stapel]

Please show steps on how you got the answer. It would help me a lot.

You already have loads of worked examples in your book, in your class notes, and in the various online lessons you've consulted. Another worked example isn't likely to make much of a difference, especially if you're completely unable even to attempt to get started. Instead, let's try to work through this exercise together.

1) A particle is moving along a horizontal line according to the equation

A "horizontal" line is one that is sideways, like the lines on a sheet of notebook paper. The particle is thus moving to the right and to the left, back and forth.

s = 2t^3 - 4t^2 + 2t - 1

This is an equation which relates the position, s, to the left or right, of the particle at time t.

a. Determine the intervals of time when the particle is moving to the right.

At some point, your class should have discussed the relationship between the position, s, of an item at time t and the velocity, v, of that item. In particular, the relationship is that the derivative, s'(t), of the position function is the velocity function, v(t). In this case, since the particle is moving to the left and to the right, then the velocity will be positive (rightward) or negative (leftward) -- or zero, of course, when the particle is stopped.

So what do you think you can do with this information?

Please be complete. Thank you!