Find critical numbers for a trig function

**Periwinkle38** · December 13th 2012, 11:16 AM

Find any critical numbers for f(x) = 2sec(x) + tan(x), 10 pi < x < 12 pi.

When I derived it I got: f'(x) = 2(sec(x))(tan(x)) + sec²(x)
I simplified it to: f'(x) = sec(x)(2tan(x) + sec(x))

I need help with what to do after this step.
Thank you for your help in advance!

**skeeter** · December 13th 2012, 02:28 PM

get f' in terms of sine and cosine ...

$f'(x) = \frac{2\sin{x}+1}{\cos^2{x}} = 0$

$\sin{x} = -\frac{1}{2}$

**Periwinkle38** · December 16th 2012, 04:13 PM

Ok so x would be 7pi/6 and 11pi/6.

I tried plugging it into the original equation but I didn't get my answer choices which are:
63pi / 6
71pi / 6
67pi / 6
73pi/ 6

**skeeter** · December 16th 2012, 04:41 PM

Originally Posted by Periwinkle38

Ok so x would be 7pi/6 and 11pi/6.

I tried plugging it into the original equation but I didn't get my answer choices which are:
63pi / 6
71pi / 6
67pi / 6
73pi/ 6

did you pay attention to the domain restriction?

Find any critical numbers for f(x) = 2sec(x) + tan(x), 10 pi < x < 12 pi.

$\color{red}\frac{60\pi}{6} < x < \frac{72\pi}{6}$

so, what are the angles in the given interval co-terminal with $\frac{7\pi}{6}$ or $\frac{11\pi}{6}$ ?

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