1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Intervals of increase/decrease of secx.

  1. Nov 4, 2012 #1
    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. jcsd
  3. Nov 4, 2012 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  4. Nov 4, 2012 #3
    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?
     
  5. Nov 4, 2012 #4
    Except at pi/2 where there is a vertical asymptote.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook