Results 1 to 3 of 3

Math Help - App of derivatives... Max and min problem solving

  1. #1
    Newbie
    Joined
    Sep 2006
    Posts
    24

    App of derivatives... Max and min problem solving

    Two sides of a Triangel have lengths of A and B, and the angle between them is Theta what value of Theta will maximixe the triagle's area? HINT
    A=(1/2)AB sin Theta

    so where do i start?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by cyberdx16 View Post
    Two sides of a Triangel have lengths of A and B, and the angle between them is Theta what value of Theta will maximixe the triagle's area? HINT
    A=(1/2)xy sin Theta

    so where do i start?
    Actually you do not need derivatives.
    When is,
    A(\theta)=\frac{1}{2}xy \sin \theta maximized?
    When the sin of the angle is maximized, when is that?
    When \sin \theta=1 (that is largest value of sine function).
    That happens when \theta=\frac{\pi}{2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by cyberdx16 View Post
    Two sides of a Triangel have lengths of A and B, and the angle between them is Theta what value of Theta will maximixe the triagle's area? HINT
    A=(1/2)AB sin Theta

    so where do i start?
    The maximum area will be where the derivative of the area function is 0. (Note: we also get minima from this so we need to prove that we actually have a maximum.)

    A' = (1/2)AB cos(theta)

    Setting this to zero we get
    cos(theta) = 0

    which happens at theta = pi/2, 3*pi/2 rad.

    The 3*pi/2 rad angle is ridiculously large for a triangle, so use theta = pi/2 rad. Is this point a local maximum? You can either do the second derivative test (ie show that A''(pi/2) < 0 ) or simply look at the graph of A(theta) at pi/2. It turns out that this is a maximum for the function.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help solving derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 17th 2011, 08:08 PM
  2. Replies: 1
    Last Post: July 17th 2010, 06:04 PM
  3. Derivatives problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2010, 02:19 AM
  4. Replies: 4
    Last Post: January 15th 2010, 08:23 AM
  5. Help Solving Derivatives?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 12th 2009, 10:27 AM

Search Tags


/mathhelpforum @mathhelpforum