Intervals of increase/decrease of secx.

[dylanhouse]

Homework Statement

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

Homework Equations

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?

 

[jbunniii]

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?

Now pick a point in each of the following intervals: [itex](-\pi/2, 0)[/itex], [itex](0, \pi)[/itex], [itex](\pi, 3\pi/2)[/itex] 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 [itex](-\pi/2, 3\pi/2)[/itex] where [itex]\sec(x)[/itex] is undefined. So, in particular, the function can't be increasing or decreasing at that point.

 

[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?

 

[dylanhouse]

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