CPM Homework Help : CALC Problem 11-129

Multiple Choice: A point traveling along the $x$ -axis has position

$s(t) = 2t^3 − 4t^2 + 2t + 1.$

The total distance traveled by the point from $t = 0$ to $t = 2$ is:

$4.593$

$6.296$

$6.593$

Hint:

Take the derivative and use it to determine when the point changes directions.
The point changes direction when $t =\frac{1}{3}$ and $t = 1$ .
total distance $=s\Big(\frac{1}{3}\Big)-s(0)-\Bigg(s(1)-s\Big(\frac{1}{3}\Big)\Bigg)+s(2)-s(1)$