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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

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    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.
     
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