CALCULUS BC
posted by paul on .
a particle moves on the xaxis in such a way that its position at time t is given by x(t)=3t^525^3+60t. for what values of t is the particle moving to the left.
a.2<t<1 only
b.2<t<1 and 1<t<2
c.1<t<2 only
d.1<t<1 and t>2
e.t<2,1<t<1, and t>2

Assuming there is a typo and the original function is:
x(t)=3t^525t^3+60t
The derivative is:
x'(t)=15*t^475*t^2+60
Factor x'(t) and solve for the zeroes of x'(t)=0.
Determine on which interval(s) x'(t) is negative, which means that the particle is moving "backwards", or to the left.
Hint:
There are two such intervals, and two of the zeroes of x'(t) are t=1 and +1.