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Math Help - Business Calc Question

  1. #1
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    Business Calc Question

    Estimate how much the function f (x) = (x / x +1 ) -3 will change as x decreases from 4 to 3.8

    If anyone could explain this, that would be great..practice problem for a test coming up.

    I got -0.008 would like to check it.


    Also have another question,

    find the derivative f(x) = 2x + 5 / (1 - 2x)^3
    Last edited by mkp23; October 11th 2011 at 03:41 PM.
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  2. #2
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    Re: Business Calc Question

    Quote Originally Posted by mkp23 View Post
    Estimate how much the function f (x) = (x / x +1 ) -3 will change as x decreases from 4 to 3.8

    If anyone could explain this, that would be great..practice problem for a test coming up.

    I got -0.008 would like to check it.

    agree


    Also have another question,

    find the derivative f(x) = 2x + 5 / (1 - 2x)^3

    quotient rule and chain rule ...

    f'(x) = \frac{(1-2x)^3 \cdot 2 - (2x+5) \cdot 3(1-2x)^2 \cdot (-2)}{(1-2x)^6}

    pull out the common factors from the two terms in the numerator and simplify
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  3. #3
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    Re: Business Calc Question

    Hello, mkp23!

    Estimate how much the function f(x)\,=\,\frac{x}{x +1}-3 will change
    as x decreases from 4.0 to 3.8

    If anyone could explain this, that would be great . . .
    . . practice problem for a test coming up.

    I got -0.008 would like to check it. . Correct!

    The key word is "estimate" ... meaning we're dealing with differentials.


    We have: . f(x) \:=\:\frac{x}{x+1}

    Then: . df \:=\:\left[\frac{(x+1)\!\cdot\!1 - x(1)}{(x+1)^2} - 0\right]\,dx \quad\Rightarrow\quad df \:=\:\frac{dx}{(x+1)^2}


    We are given: . x = 4,\;\;dx = -0.2

    Therefore: . df \;=\;\frac{-0.2}{(4+1)^2} \;=\;-0.008 .(approximate change)


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    We can compare it to the actual change of f(x).

    f(4) \:=\:\frac{4}{5} - 3 \;=\;-2.2

    f(3.8) \:=\:\frac{3.8}{4.8} -3 \;=\;-2.208333\hdots

    The actual change is: . \Delta f \;=\;(-2.208333) - (-2.2) \;=\;-0.008333\hdots

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