How to Find the Maximum and Minimum Speed of a Particle?

[hellboy324]

Homework Statement

The position vector of a particle at time t is given by r(t)= 2sin(2t)i + cos(2t)j + 2tk where t >=0.

Homework Equations

v(t) = 4cos(2t)i - 2sin(2t)j + 2k
speed = | v(t) | =√(16cos^2(2t)+4sin^2(2t)+4) = √(12cos^2(2t)+8)

The Attempt at a Solution

I found the velocity and speed, but I have no idea what to do to find out the maximum and minimum speed for this question, someone can teach me?

 

[vela]

How do you usually find the extrema of a function?

 

[Hat1324]

Things are easier in that the question is asking about scalar speed. What does it mean for the derivative when speed hits a peak/trough?