# Homework Help: Intervals of increase/decrease of secx.

1. Nov 4, 2012

### dylanhouse

1. The problem statement, all variables and given/known data

Find the intervals of increase and decrease of secx on the interval (-pi/2, 3pi/2).

2. Relevant equations

3. The attempt at a solution

I found the derivative and set it equal to zero to get the critical points:
f'(x)=sinx/cos^2x
0=sinx/cos^2x
0=sinx
x= 0 and pi (restricted by interval)

Now to find the intervals of increase and decrease I am lost? It says think about the unit circle?

2. Nov 4, 2012

### jbunniii

Now pick a point in each of the following intervals: $(-\pi/2, 0)$, $(0, \pi)$, $(\pi, 3\pi/2)$ and evaluate the derivative at those points. How can you use this to determine where the function is increasing or decreasing?

Also, note that there is one point in $(-\pi/2, 3\pi/2)$ where $\sec(x)$ is undefined. So, in particular, the function can't be increasing or decreasing at that point.

3. Nov 4, 2012

### dylanhouse

I evaluated -pi/4 < 0, pi/2 >0 and 5pi/4 < 0. This would mean a decrease from -pi/2 to 0 and pi to 3pi/2. And an increase from 0 to pi?

4. Nov 4, 2012

### dylanhouse

Except at pi/2 where there is a vertical asymptote.