# Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 04 (a)/Solution 1

First, we find ${\displaystyle x'(0)}$.
Since we have the differential equation ${\displaystyle x'(t)=rx(t)(1-(x(t))^{2})}$, plugging ${\displaystyle t=0}$ and using ${\displaystyle x(0)=3}$, we get
${\displaystyle x'(0)=rx(0)(1-(x(0))^{2})=3r(1-3^{2})=-24r}$
Then, by its definition in the Hint, we get the speed of the particle at ${\displaystyle t=0}$ as ${\displaystyle \color {blue}|x'(0)|=24r}$.