# Thread: Critical numbers of Trig functions

1. ## Critical numbers of Trig functions

Find the critical numbers on 0 < x < 2

$\displaystyle f(x) = 4x - 4tan(x)$
$\displaystyle f'(x) = 4 - sec^2(x)$

f'(x) is undefined at $\displaystyle \frac{\pi}{2}$ and $\displaystyle \pi + \frac{\pi}{2}$

I figured the next answer was $\displaystyle \frac{\pi}{3}$ and $\displaystyle \pi + \frac{\pi}{3}$ because that makes the derivative 0, but $\displaystyle n\pi + \frac{\pi}{3}$ isn't in the domain of the original function.

So how would I go about finding the 0's?

2. Originally Posted by Open that Hampster!
Find the critical numbers on 0 < x < 2

$\displaystyle f(x) = 4x - 4tan(x)$
$\displaystyle f'(x) = 4 - sec^2(x)$

correction ... $\displaystyle \textcolor{red}{f'(x) = 4 - 4\sec^2{x}}$
yes, the original function and, therefore, its derivative are undefined at $\displaystyle x = \frac{\pi}{2}$

$\displaystyle 4(1-\sec^2{x}) = 0$

$\displaystyle \sec^2{x} = \pm 1$

only solution in the interval [0,2] is x = 0

3. Ugh, I was messing the the math tags and it must have disappeared.

The upper bound is 2 pi, not 2.

4. Originally Posted by Open that Hampster!
Ugh, I was messing the the math tags and it must have disappeared.

The upper bound is 2 pi, not 2.
ok, then ...

the original function and its derivative are undefined at $\displaystyle x = \frac{\pi}{2}$ and $\displaystyle x = \frac{3\pi}{2}$

$\displaystyle \sec^2{x} = \pm 1$ at $\displaystyle x = 0$ , $\displaystyle x = \pi$ , and $\displaystyle x = 2\pi$