What Are the Critical Numbers for the Function f(θ) = 2sec(θ) + tan(θ)?

[jeonw]

Homework Statement

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

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]

The expression can be further simplified:
$$\sec^{2}x(2\sin x+1)=0$$
as sec(x) is never zero, we can divide through by it and not loose any solutions. What are you left with?

 

[timon]

$$sec(x)[2tan(x)+sec(x)] = 0$$

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

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

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