CPM Homework Help : APCALC Problem 11-114

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.

More Help:

The point changes direction when $t = 1/3$ and $t = 1$ .

Step:

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