Consider the following.

$r(t)=($:$4t,t^2,\frac{1}{6}{t}^3$:$)$

Find $r^{\text{'}}(t).$

$r^{\text{'}}(t)=$

Well done!

Find $|r^{\text{'}}(t)|$ for $0t1.$

$|r^{\text{'}}(t)|=$

$$

Find the length of the curve.

$r(t)=($:$4t,t^2,\frac{1}{6}{t}^3$:$),0t1$