Results 1 to 3 of 3

Math Help - Basic Derivative Problem

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    2

    Basic Derivative Problem

    Greeting MHF, first timer here.

    I've been taking Calculus over the summer and I've stumbled upon a question that I need assistance with.. Your help is greatly appreciated

    DIRECTIONS: Find the equation of the tangent line to the given function at the given point using: limit h->0 (f(x+h)-f(x))/h

    Problem: f(x)= sqrt(x-1), (5,2)

    What I've done to try and solve this:

    Limit h->0 (sqrt(x+h-1) - sqrt (x-1))/h

    Then I tried to multiply the numerators conjugate to both the numerator and the denominator so it looks like now (or at least to me):

    limit h->0 (x+h-1-x-1)/h(sqrt(x+h-1)+sqrt(x-1))

    Then It simplifies to:

    limit h->0 (h-2)/h/h(sqrt(x+h-1)+sqrt(x-1))

    but when you use direct substitution to find the slope you get -2/0, which isnt possible..

    Where have I gone wrong? Any help is greatly appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,882
    Thanks
    672

    Re: Basic Derivative Problem

    \lim_{h \to 0} \frac{\sqrt{(x+h)-1} - \sqrt{x-1}}{h}

    \lim_{h \to 0} \frac{\sqrt{(x+h)-1} - \sqrt{x-1}}{h} \cdot \frac{\sqrt{(x+h)-1} + \sqrt{x-1}}{\sqrt{(x+h)-1} + \sqrt{x-1}}

    \lim_{h \to 0} \frac{(x+h)-1 - (x-1)}{h \left[\sqrt{(x+h)-1} + \sqrt{x-1}\right]}

    \lim_{h \to 0} \frac{h}{h \left[\sqrt{(x+h)-1} + \sqrt{x-1}\right]}

    now finish it ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    2

    Re: Basic Derivative Problem

    From that last equation you can cancel out the h's on the outside so you get

    lim h->0 1/(sqrt(x-h+1)+sqrt(x-1)

    Direct substitution and you get m=1/4

    Thanks. I was able to get the equation using point slope.

    Your help was greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basic and easy Derivative question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 8th 2010, 02:58 PM
  2. Basic Derivative Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 10th 2009, 10:16 AM
  3. Basic Transform of Derivative Help?
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: April 13th 2009, 08:46 PM
  4. Basic derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 10th 2009, 05:40 AM
  5. Basic Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 15th 2007, 06:00 PM

Search Tags


/mathhelpforum @mathhelpforum