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: Critical Points

  1. Jun 19, 2011 #1
    1. The problem statement, all variables and given/known data
    g(x) = 4x - tanx
    2. Relevant equations

    3. The attempt at a solution
    [tex]g(\theta) = 4\theta - tan\theta[/tex]
    [tex]\theta = arctan0[/tex]
    [tex]\theta = k\pi[/tex]

    So, that lists the zeros of the derivative if I am correct. I believe the other critical points are pi/2 + kpi, where tan is undefined. That is all of the critical points correct?
  2. jcsd
  3. Jun 19, 2011 #2
    You made an error:

    We have cos² θ + sin² θ = 1, but 4 cos² θ - 1 = 4 (1 - sin² θ) - 1 = 3 - 4 \sin² θ.

    Instead you should simply set

    4 cos² θ - 1 = 0,

    which gives you cos θ = ±½.
  4. Jun 19, 2011 #3
    Thank you, yeah I caught that right after I posted. Now I am stuck on another problem. I suppose this should more or less be posted in the pre-calc/trig section.

    Finding the critical points of:


    I just know there is a pythag. identity in there somewhere to aid in solving for 0.
  5. Jun 19, 2011 #4
    Well, just express the cosine by the sine using the Pythagorean identity to get f'(x) = -2 sin x + 2 - 4 sin² x, which is a polynomial in z = sin x with roots z = -1/4 ± 3/4. Then you calculate the x corresponding to those values of sin x. That's a standard trick to solve trigonometric equations - if you have odd powers of only one trigonometric function (here sin), express the other (here cos) and you get a polynomial in the first trig function.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook