Find Critical numbers

**unluckykc** · October 31st 2007, 09:57 PM

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).

**Jhevon** · October 31st 2007, 09:59 PM

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 $\sec \theta$ and $\tan \theta$ ?

**unluckykc** · October 31st 2007, 10:08 PM

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}

**Jhevon** · October 31st 2007, 10:14 PM

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 $\sec \theta$ is never zero, correct?

anyway, here's how i would proceed.

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

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

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

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