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Math Help - Newbie to Derivative needs help

  1. #1
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    Newbie to Derivative needs help

    There are 2 problems I am having particular trouble with.

    QUESTION 1

    A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration, C(x), in parts per million, is given approximately by C(x)= 0.1/x^2 where x is the distance from the plant in miles.

    So the derivative is -.2x^-3 i believe?

    And then I have to evaluate C(2) and C'(2).

    C(2) = -.2(2)^3 = -.025

    C'(2) = I am unsure of how to acquire this.


    QUESTION 2

    Use the definition of the derivative to find f'(x) if f(x) = x^3.

    I know the derivative is 3x^2 but when I try to do it step by step by hand I get screwed up somewhere.

    Any help or tips in the right direction would be appreciated.
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  2. #2
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    Quote Originally Posted by Zabulius View Post
    There are 2 problems I am having particular trouble with.

    QUESTION 1

    A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration, C(x), in parts per million, is given approximately by C(x)= 0.1/x^2 where x is the distance from the plant in miles.

    So the derivative is -.2x^-3 i believe?

    correct ... C'(x) = -\frac{0.2}{x^3}

    And then I have to evaluate C(2) and C'(2).

    C(2) = -.2(2)^3 = -.025

    no ... C(2) = \frac{0.1}{2^2}

    C'(2) = I am unsure of how to acquire this.

    C'(2) = -\frac{0.2}{2^3}


    QUESTION 2

    Use the definition of the derivative to find f'(x) if f(x) = x^3.

    below ...
    f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3

    f(x) = x^3

    f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

    f'(x) = \lim_{h \to 0} \frac{(x^3 + 3x^2h + 3xh^2 + h^3) - (x^3)}{h}

    f'(x) = \lim_{h \to 0} \frac{3x^2h + 3xh^2 + h^3}{h}

    f'(x) = \lim_{h \to 0} \frac{h(3x^2 + 3xh + h^2)}{h}

    f'(x) = \lim_{h \to 0} (3x^2 + 3xh + h^2) = 3x^2
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  3. #3
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    Much appreciated skeeter!
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