### Home > CALC > Chapter 11 > Lesson 11.4.1 > Problem11-129

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:

1. $4$

1. $5$

1. $4.593$

1. $6.296$

1. $6.593$

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 $=s\Big(\frac{1}{3}\Big)-s(0)-\Bigg(s(1)-s\Big(\frac{1}{3}\Big)\Bigg)+s(2)-s(1)$