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Adv. Functions: Rate of Change in Rational Functions

  1. Sep 29, 2014 #1
    1. The problem statement, all variables and given/known data
    mtan for f(x) = 5/√ 3x ... at x=1

    2. Relevant equations
    msec = y2-y1 / x2-x1

    3. The attempt at a solution
    The two points I got from the equation: (1, 5/√ 3) and (1+h, 5/√ 3+h)

    msec = f(1+h) - f(1) / h
    = (5/√ 3+h - 5/√ 3) / h ... multiply top and bottom by denominators (√ 3+h) and (√ 3)
    = 5√ 3 - 5√ 3+h / h(√ 3+h)(√ 3) ... multiply top and bottom by the conjugate (5√ 3 + 5√ 3+h)
    = 25√ 9 + 25√ 9+h - 25√ 9+h - 25√ 9+h2 / h(√ 3+h)(√ 3)(5√ 3+5√ 3+h)
    = 25√ 9 - 25√ 9+h2 / h(√ 9+h)(5√ 3+5√ 3+h)
    = 75 - 25√ 9+h2 / h(5√ 27+3h + 5√ 27+3h2)

    No idea if this is right and where I'm going with this.
    I don't know the answer to this question either, so can't check my work...
     
  2. jcsd
  3. Sep 29, 2014 #2

    Mark44

    Staff: Mentor

    Please clarify what you're saying here. Which if these is your function?
    $$1. f(x) = \frac{5}{\sqrt{3}}x$$
    $$2. f(x) = \frac{5}{\sqrt{3x}}$$
    $$3. f(x) = \frac{5}{\sqrt{3}x}$$
     
  4. Sep 29, 2014 #3
    Oh, the second one.
    $$2. f(x) = \frac{5}{\sqrt{3x}}$$
    Sorry about that!
     
  5. Sep 29, 2014 #4

    Mark44

    Staff: Mentor

    You need more parentheses.
    The second point should be written as (1 + h, 5/√(3 + h)), otherwise the 2nd coordinate looks like this:
    $$ \frac{5}{\sqrt{3}} + h$$
    The right side should be written as (f(1 + h) - f(1))/h. Most would interpret what you wrote as
    $$ f(1 + h) - \frac{f(1)}{h}$$
    You have the right idea, but with all the missing parentheses, it's just too hard to read.
     
  6. Sep 29, 2014 #5

    Mark44

    Staff: Mentor

    When it's completely simplified, you should get this:
    $$ \frac{-5\sqrt{3}}{6}$$

    BTW, LaTeX makes it much easier to read, and isn't that hard to write.
    To create a fraction, do this:
    Code (Text):
    \frac{a + b}{c}
    I don't show the pairs of $ symbols at front and back.
    This renders like so:
    $$\frac{a + b}{c}$$

    To create a square root, do this:
    Code (Text):
    \sqrt{3 + h}
    Again, you need $ pairs at front and back.
    This is how it looks in the browser:
    $$\sqrt{3 + h}$$
     
    Last edited: Sep 29, 2014
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