Results 1 to 3 of 3

Math Help - First derivative test, local min/max

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    69

    First derivative test, local min/max

    Hi

    I have a function

    g(x)=(cos \ x + sin \ x -  1)e^{cos x + sin x} \ \ \ \ \      (0 \leq x \leq\pi)

    the derivative being

    g`(x)=(cos^2 \ x - sin^2 \ x)e^{cos x + sin x}

    I'm not sure how to find the turning point within this domain.

    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    12
    g'(x)=\left( \cos ^{2}x-\sin ^{2}x \right)e^{\cos x+\sin x}=0, and this is just \cos ^{2}x-\sin ^{2}x=0 since e^{\cos x+\sin x}>0 for each x\in\mathbb R. Now find solutions for 0\le x\le\pi for that trig. equation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    This could simply things.
    \cos ^2 (x) - \sin ^2 (x) = \cos (2x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 21st 2011, 01:23 AM
  2. Replies: 6
    Last Post: January 5th 2011, 02:34 AM
  3. Replies: 4
    Last Post: December 13th 2010, 12:17 PM
  4. Replies: 3
    Last Post: March 1st 2009, 03:27 PM
  5. First Derivative Test for Local Extrema
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 14th 2008, 09:10 PM

Search Tags


/mathhelpforum @mathhelpforum