1. ## Find Critical numbers

Find any critical numbers of: f(theta) = 2sec(theta) + tan(theta), 0<theta<2pi.
I found the defivative, but I got stuck.

I got to 2tan(theta)=-sin(theta).

2. Originally Posted by unluckykc
Find any critical numbers of: f(theta) = 2sec(theta) + tan(theta), 0<theta<2pi.
I found the defivative, but I got stuck.

I got to 2tan(theta)=-sin(theta).
and how did you get to that answer? what is the derivative of $\displaystyle \sec \theta$ and $\displaystyle \tan \theta$?

3. Oh, sorry. I got to include the steps.
f'(theta) = 2sec(theta)tan(theta) + sec^2(theta)
I set it equal to zero, factored out a sec(theta). I was left with 2 equations: sec(theta)=0 and 2tan(theta) + sec(theta) = 0 =>2tan(theta) = -sec(theta) {I didn't mean sin before...I meant sec}

4. Originally Posted by unluckykc
Oh, sorry. I got to include the steps.
f'(theta) = 2sec(theta)tan(theta) + sec^2(theta)
I set it equal to zero, factored out a sec(theta). I was left with 2 equations: sec(theta)=0 and 2tan(theta) + sec(theta) = 0 =>2tan(theta) = -sec(theta) {I didn't mean sin before...I meant sec}
ok. and you are aware that $\displaystyle \sec \theta$ is never zero, correct?

anyway, here's how i would proceed.

$\displaystyle 2 \tan \theta + \sec \theta = 0$

$\displaystyle \Rightarrow \frac {2 \sin \theta }{\cos \theta} + \frac 1{\cos \theta } = 0$

now combine the fractions and set the numerator equal to zero and solve for theta