Critical numbers of Trig?

1. The problem statement, all variables and given/known data

f(theta)=2sec(theta)+tan(theta)

3. The attempt at a solution
I found the derivative and set it equal to zero and to reduce writing I substituted x for theta
f'(x)=2sec(x)tan(x)+sec^2(x)
sec(x)[2tan(x)+sec(x)]=0

My question is what are the critical numbers? do the critical numbers exist where sec(x) is underfined because sec(x) will never equal 0.
 

hunt_mat

Homework Helper
1,669
11
The expression can be further simplified:
[tex]
\sec^{2}x(2\sin x+1)=0
[/tex]
as sec(x) is never zero, we can divide through by it and not loose any solutions. What are you left with?
 
56
0
[tex] sec(x)[2tan(x)+sec(x)] = 0[/tex]

You are trying to find an x to make the left side equal to 0.

Like you said, there is no x for which [tex]sec(x) = 0[/tex], so you can discard that possibility.

How else can the left side of that equation be 0?
 

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