1. Not finding help here? Sign up for a free 30min 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!

Finding Relative Extrema & Points Of Inflection

  1. Mar 24, 2004 #1

    Cod

    User Avatar

    For the function below, I have to find the exact values of x for which relative extreme exist and the exact values of x for which points of inflection exist.

    [tex]f(x) = 1x/2 - sin(x)[/tex] when x is in the interval [tex](0,2pi)[/tex]

    Here's what I have:

    [tex]f'x = 1/2 - cos(x) = 0[/tex] (I'm not sure how to solve for x in this spot)

    Also, for the finding the inflection points, I have this:

    [tex]f"x = sin(x) = 0[/tex]

    [tex]x = 0/sin = 0[/tex] (This right? Or did I screw up before this?)



    I guess my troubles are based around the basic trig functions as well as algebra. I'm in the process of moving, so my algebra book will be hard to find; however, I'm about to start looking.

    Any help to point me in the right direction would be fantastic. Thanks.
     
    Last edited: Mar 24, 2004
  2. jcsd
  3. Mar 24, 2004 #2

    ShawnD

    User Avatar
    Science Advisor

    First of all, wtf is up with your post? It there's a big black area and I can see some of the page's source code.

    [tex]f'(x) = \frac{1}{2} -cos(x) = 0[/tex]

    [tex]cos(x) = \frac{1}{2}[/tex]

    You can either cheap out and use your calculator or you can draw those goofy triangles. HERE is the one that applies in this case.
    Turn 60 degrees into radians by dividing by 180 then multiplying by pi.

    [tex]x = \frac{\pi}{3}[/tex]


    I can't even read what you have for inflection stuff because of the black area I mentioned.

    [tex]f''(x) = sin(x) = 0[/tex]

    [tex]x = 0, \pi , 2\pi[/tex]

    That is NOT the answer though! The interval is between 0 and 2[tex]\pi[/tex] but those are rounded brackets. Round brackets mean you do NOT include the limits, that means 0 and 2[tex]\pi[/tex] are not answers.

    [tex]x = \pi[/tex]
     
  4. Mar 24, 2004 #3
    I have a program that finds roots. First extremum x is a little more than 1 radian and second about 5.20
     
  5. Mar 24, 2004 #4

    ShawnD

    User Avatar
    Science Advisor

    Excellent point.

    cos(x) = 1/2 is a referance angle. The first correct answer is pi/3. The second answer is mirrored around the x axis (sine is mirrored around the y axis). The second answer should be 2pi - pi/3 which is 5pi/3 (about 5.23 as beyond had said).
     
  6. Mar 25, 2004 #5

    Cod

    User Avatar

    Thanks for the help fellas. I don't know why my post looks like that. I checked it about 20 times looking for a mistake in the Latex coding, but there aren't any.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Finding Relative Extrema & Points Of Inflection
  1. Relative extrema (Replies: 4)

Loading...