# Thread: Critical numbers

1. ## Critical numbers

This is just a practice quiz, but I want to know how to do it for when I take the test. Here is my question:

http://i42.tinypic.com/im3q53.jpg

Thanks!

EDIT: I meant I graphed it as 2(1/cosx) +tanx

2. $\displaystyle \frac{d}{dx}(2\sec \theta + \tan \theta)=\frac{1}{\cos ^2 x}(2\sin x +1)=0 \Longleftrightarrow \sin x = -\frac{1}{2}$

3. convert to sines and cosines

2sin(t) = -1

t= 7pi/6 and 11pi/6

Seems who ever made the answer key was trying to be cute --A and B are coterminal with 7pi/6 and 11pi/6

Technical point -- a stationary point is where the derivative is 0

A critical point is where the derivative is either 0 or undefined

The point is a critical point represents where the sign of the derivative can change signs either where it is 0 or undefined

For example |x| has a critical point at 0 even though it has no derivative there

Also the derivative is undefined at pi/2 which would make it a critcal number also this would make c a viable answer as well

4. Correction

Since f is not defined at pi/2 --it is not a critical point

|x| is defined at 0 but its derivative is not