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

First, we find $x'(0)$.

Since we have the differential equation $x'(t)=rx(t)(1-(x(t))^{2})$, plugging $t=0$ and using $x(0)=3$, we get

$x'(0)=rx(0)(1-(x(0))^{2})=3r(1-3^{2})=-24r$

Then, by its definition in the Hint, we get the speed of the particle at $t=0$ as $\color {blue}|x'(0)|=24r$.