Confusion about max speed in kinematics

Question

$V=-12 \sin(3t)$ When you differentiate and equate it to $0$, you get $t=\pi/6$, but the speed at this time is $-12$, is this correct? My book has the answer positive $12$. The whole question is: A particle p moves in a straight line such that its displacement from a fixed point $0$ seconds after passing o is given by: $4\cos(3t)-4$

Answer 1

Speed is the unsigned magnitude of velocity, so just take the absolute value (drop the negative sign).

Just to add, you don't even have to differentiate the velocity function. $\sin 3t$ has a maximum magnitude of $1$, a fact you should be able to assume without calculus.