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Homework Help: Find the points on a horizontal line

  1. Sep 19, 2010 #1
    Question: Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

    f'(x)=2cos x+2sinxcosx...i think

    No idea where to go after this...
  2. jcsd
  3. Sep 19, 2010 #2


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    Ok, if the tangent line is horizontal, what does f'(x) have to be?
  4. Sep 19, 2010 #3
    f'(x)=2cosx +2sinx*(sinx)d/dx
    =2cosx +2sinx*cosx
    =cos (2+2sinx)
  5. Sep 19, 2010 #4


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    Hi there, the first thing that I would do is to factor out the 2cos(x).

    1. 2cosx(sinx + 1) = 0

    Note that this has to be equal to zero because when a tangent line is horizontal it has to be zero.

    So all you have to do is find when sinx = -1 OR cosx = 0 on [0,2π)
    So x can either be (3π)/2 (that's when sin(x) = -1) or π/2 (that's when cos(x) = 0).

    I double checked this with my graphing calculator and these points are also the relative maxima, where the tangent line is 0.
  6. Sep 19, 2010 #5
    Thank you so much:) I really appreciate it:)
  7. Sep 19, 2010 #6


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    And just to show it it visually so you can fully understand:[PLAIN]http://img818.imageshack.us/img818/2223/mathp.png [Broken]
    Last edited by a moderator: May 4, 2017
  8. Sep 19, 2010 #7
    Oh, ok:) that makes sense:) Thank you:)
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