Results 1 to 7 of 7

Math Help - Slope of a tangent line and weird world problem

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    5

    Slope of a tangent line and weird world problem

    Three problems:

    1) find the slope of the tangent line for the graph f(x)= x^2 at (2,4).

    2) Find the slope of the line joining (2,4) and (2+h, f(2+h)) in terms of the nonzero number h. (This is also for the graph f(x)= x^2)

    And

    A rancher has 300 feet of fence to enclose two adjacent pastures. (See figure) Express the total area A of the two pastures as a function of x. What is the domain of A?

    Graph the area function (I suppose I can do this once I find the equation) and estimate the dimensions that yield the maximum amount of area for the pastures.

    Find the dimensions that yield the maximum amount of area for the pastures by completing the square.

    THANKS for reading this and trying to help
    Attached Thumbnails Attached Thumbnails Slope of a tangent line and weird world problem-figure.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by superfly8912 View Post
    Three problems:

    1) find the slope of the tangent line for the graph f(x)= x^2 at (2,4).
    Find f'(2)

    Spoiler:
    f(x) = x^2 \Rightarrow f'(x) = 2x \Rightarrow f'(2) = 2\times 2 = 4
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by superfly8912 View Post

    2) Find the slope of the line joining (2,4) and (2+h, f(2+h)) in terms of the nonzero number h. (This is also for the graph f(x)= x^2)
    Let the slope of the line be m.

    Find m = \frac{f(2+h)-f(4)}{2+h-2}

    Spoiler:
    m = \frac{f(2+h)-f(4)}{2+h-2} = \frac{(2+h)^2-(4)^2}{h} =\frac{4+4h+h^2-16}{h} =\frac{4h+h^2-12}{h}



    Quote Originally Posted by superfly8912 View Post

    A rancher has 300 feet of fence to enclose two adjacent pastures. (See figure) Express the total area A of the two pastures as a function of x. What is the domain of A?

    Graph the area function (I suppose I can do this once I find the equation) and estimate the dimensions that yield the maximum amount of area for the pastures.

    Find the dimensions that yield the maximum amount of area for the pastures by completing the square.
    Consider the perimeter of the fence.

    x+x+x+y+y+y+y = 300

     3x+4y = 300

    Rearrange for y

     y = \frac{300-3x}{4}

    Now Area = 2xy as there are 2 pastures

     A= 2xy = 2x\frac{300-3x}{4} =\frac{600x-6x^2}{4}

    Now graph this function. It is a quadratic so you can find the turning point (or the maximum) using symmetry.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2009
    Posts
    5
    Thank you for helping me out but I'm having trouble. Why did you square the numerator in number two? I happen to have the answer for this problem and apparently its 4 + h (but then again it could be a typo)...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by superfly8912 View Post

    2) Find the slope of the line joining (2,4) and (2+h, f(2+h)) in terms of the nonzero number h. (This is also for the graph f(x)= x^2)
    f(x)= x^2 \Rightarrow f(2+h) = (2+h)^2 = (2+h)(2+h) = 4+4h+h^2
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by pickslides View Post
    Let the slope of the line be m.

    Find m = \frac{f(2+h)-f(4)}{2+h-2}
    Should be:
     m = \frac{f(2+h)-f(2)}{2+h-2} = \frac{(2+h)^2 - (2)^2}{h} = \frac{h^2 + 4h + 4 - 4}{h} = h+4
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by Defunkt View Post
    Should be:
     m = \frac{f(2+h)-f(2)}{2+h-2} = \frac{(2+h)^2 - (2)^2}{h} = \frac{h^2 + 4h + 4 - 4}{h} = h+4
    Yes I see... Nice work Defunkt!

    Or even easier again

    m = \frac{f(2+h)-4}{2+h-2} = \frac{(2+h)^2 - 4}{h} = \frac{h^2 + 4h + 4 - 4}{h} = h+4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 12th 2011, 03:38 PM
  2. Real World Problem - Integrating Slope Data!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 6th 2010, 09:17 PM
  3. slope of the tangent line?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 19th 2010, 05:02 PM
  4. Slope of Tangent Line
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2009, 04:20 PM
  5. Secant Line Slope and Tangent Line Slope
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 26th 2009, 06:40 PM

Search Tags


/mathhelpforum @mathhelpforum