Find critical numbers for a trig function

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)) + sec^{2}(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!

Re: Find critical numbers for a trig function

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

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

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

Re: Find critical numbers for a trig function

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

Re: Find critical numbers for a trig function

Quote:

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?

Quote:

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

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

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