Results 1 to 3 of 3

Math Help - maxima and minima

  1. #1
    Newbie
    Joined
    Feb 2008
    From
    Makati, Philippines
    Posts
    3

    Post maxima and minima

    i really need help for the following problems in finding their maxima and minima

    1. a rectangular box with a square box has the top and bottom made of one material while the sides are made of a different material which costs twice as much. the volume is 100 cubic cm. find the dimensions so that the cost of production would be as low as possible.

    2. Leo is at pt. A walking eat at 2m/s. Aya who is 60 m North East of Leo starts walking North at the same instant at the rate of 3 m/s. how fast are they separating one minute later?

    3. f(x) = 2 sin(3x)


    and i know this sounds dumb, but how would u solve

    (-x^2 + 2x + 2 ) / (x^2 + 2) ^2 = 0


    thanks very much if you can help...>.< im going crazy over this. if anyone can solve any of the problems please...even if just one is solved..
    Last edited by icyxbluxkitty; February 24th 2008 at 10:58 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by icyxbluxkitty View Post
    and i know this sounds dumb, but how would u solve

    (-x^2 + 2x + 2 ) / (x^2 + 2) ^2 = 0

    You can multiply through by (x^2+2)^2 to get:

     -x^2 + 2x + 2  = 0

    Then solve the quadratic.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,806
    Thanks
    116
    Quote Originally Posted by icyxbluxkitty View Post
    ...

    1. a rectangular box with a square box (do you mean bottom) has the top and bottom made of one material while the sides are made of a different material which costs twice as much. the volume is 100 cubic cm. find the dimensions so that the cost of production would be as low as possible.

    ...
    I assume that the box has a bottom like a square.

    Let x denote the length of one side of the square and h denote the height of the box.

    Then you know:
    A) volume:
    V = x^2 \cdot h = 100
    B) surface area:
    s = 2x^2+4x \cdot h
    C) costs:
    c = 2x^2 + 2 \cdot 4x \cdot h

    From A) you get: h=\frac{100}{x^2} . Plug in this term instead of h into the equation at C):

    c(x) = 2x^2 + \frac{800}{x}

    The function c(x) has an extreme value (minimum or maximum) if c'(x) = 0:

    c'(x) = 4x - \frac{800}{x^2} . Set c'(x) = 0 and solve for x:

    I've got x = \sqrt[3]{200} \approx 5.848

    Now plug in this value into the equation calculating h:

    h=\frac{100}{(\sqrt[3]{200})^2} = \sqrt[3]{\frac{1,000,000}{40,000}} = \sqrt[3]{25} = \sqrt[3]{\frac18 \cdot 200} = \frac12 \cdot  \sqrt[3]{200} and therefore h = \frac12 x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maxima and Minima
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 8th 2010, 03:59 PM
  2. Maxima and Minima
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 4th 2009, 11:10 AM
  3. Maxima and Minima
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 30th 2009, 04:06 AM
  4. Maxima and minima 3
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 28th 2009, 08:30 AM
  5. Maxima/ Minima
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 3rd 2008, 03:47 AM

Search Tags


/mathhelpforum @mathhelpforum