Question

PLEASE HELP


Suppose that the position of a particle as a function of time is given by the formula s(t)=6+7t^5-t^7, t>0

The time at which the velocity is maximum is?

Answer 1

velocity is the first derivative of position, i.e.:
\[ v(t) = \frac{d}{dt}s(t)\]

once you find the function for velocity v(t), then you can find the maximum of the function. you can do this by inspecting the graph, or by taking the derivative of v(t), which is a(t), and solve a(t) = 0 for t.

you might get more than one solution for a(t) =0 , in which case substitute the solutions into v(t) and find t out of that set of solutions that gives you the largest v(t).

Answer 2

a(t) = 0 i got sqrt(30)/3

Answer 3

what do i do next