Posted by Yoona on Sunday, November 20, 2011 at 2:37pm.
A particle moves along the caxis so that at time t its position is given by x(t)=t^26^t+9t+11
a)What is the velocity of the particle at t=0
b)During what time intervals is the particle moving to the left?
c)What is the total distance traveled by the particle t=0 to t=2

Calculus  Correction?  Steve, Sunday, November 20, 2011 at 2:53pm
I can't believe that is the correct equation of motion. 6^t will grow negative quite quickly. Since there's a typo in caxis, I suspect there's another in the equation.

Calculous  Yoona, Sunday, November 20, 2011 at 2:55pm
opps it is x(t)=t^36t^2+9t+11
Sorry!! 
Calculus  Steve, Sunday, November 20, 2011 at 4:09pm
That's better!
x(t) is the position
x'(t) is the velocity
x'(t) = 3t^2  12t + 9
x'(0) = 9
particle moving to the left means velocity is negative.
3(t^2  4t + 3) = 3(t1)(t3) < 0
when 1 < t < 3
distance traveled is x(2)  x(0) 
Calculous  Yoona, Sunday, November 20, 2011 at 4:55pm
thanks!!! that was VERY helpful!!