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Find the critical numbers of a function

  1. Oct 26, 2013 #1
    Thank you for viewing my thread. The following is a problem from my homework that is submitted online. I have already exhausted my attempts, but I'm curious as to where I went wrong. I would appreciate if someone could lead me towards the solution.
    1. The problem statement, all variables and given/known data
    Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.)
    g(θ) = 28θ − 7 tan θ
    f2acfb64dbc9f8b72b5f9d2c6e6b696f.png
    2. Relevant equations
    The critical values of a function, f, are located where f'(c) = 0 or DNE.

    3. The attempt at a solution
    g(θ) = 28θ − 7 tan θ
    g'(θ) = 28 − 7 sec(θ)^2
    0 = 4 - sec(θ)^2
    4 = sec(θ)^2, when θ = ((6*n-1)*pi) / 3

    74a99371c78723958c43625d14b4e2e6.png
     
  2. jcsd
  3. Oct 26, 2013 #2

    Zondrina

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    Homework Helper

    You have the right idea. Use an identity you know to help you:

    ##±2 = sec(θ)##
    ##±2cos(θ) = 1##
    ##cos(θ) = ±\frac{1}{2}##

    Now solve for ##θ##.
     
  4. Oct 26, 2013 #3

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    That is the same as ##2n\pi - \frac \pi 3##. I don't think you have all of them.
     
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