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    Edit: Complete

    Find the equation of the curve with the given derivative of y with respect to x that passes through the given point:

    \frac {dy}{dx} = (x+2)^2; point (1, 7)

    (x+2)(x+2) = x^2 + 4x + 4

    y = \frac {1}{3}x^3 + 2x^2 + 4x + c

    7 = \frac {1}{3} + 2 + 4 + c

    7 = \frac {1}{3} + \frac {6}{3} + \frac {12}{3} + c

    7 = \frac {19}{3} + c

    \frac {21}{3} - \frac {19}{3} = c

    c = \frac {2}{3}

    So, \frac {1}{3}x^3 + 2x^2 + 4x + \frac {2}{3}
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    sub in x=1 and set y = 7
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    (Original post by joeh37)
    sub in x=1 and set y = 7
    This, and then solve for C.
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    (Original post by im so academic)
    This, and then solve for C.
    That was implied
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    (Original post by im so academic)
    This, and then solve for C.
    7 = \frac {1}{3}x^3 + 2x^2 + 4x + c

    So would that be:

    7 = \frac {1}{3} + 2 + 4 + c

    Right?

    But how would c = \frac {2}{3}?
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    (Original post by Mr Inquisitive)
    7 = {1}{3}x^3 = 2x^2

    So would that be:

    7 = 1 + 1 + 4 + c

    Right?

    But how would c = \frac {2}{3}?
    y = 1/3 + 2 + 4 + c

    7 = 19/3 + c

    Then rearrange to find c. (which is 2/3).

    Substitute the value for c in f(x) to get the equation.
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    (Original post by im so academic)
    y = 1/3 + 2 + 4 + c

    7 = 19/3 + c

    Then rearrange to find c.
    Ahh, thank you.
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    (Original post by Mr Inquisitive)
    Ahh, thank you.
    Remember though that is not the answer as the question specifically states to write down the equation.
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    Hi GUYS IM MR INQUISITIVE AND

    1 TIMES 2 = ...


    ... 1!!!???




    What the ****.
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    (Original post by im so academic)
    Remember though that is not the answer as the question specifically states to write down the equation.
    Just the y = \frac{1}{3}x^3 + 2x^2 + 4x + \frac {2}{3} then?
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    (Original post by Mr Inquisitive)
    Just the y = \frac{1}{3}x^3 + 2x^2 + 4x + \frac {2}{3} then?
    :yep:
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    (Original post by M Loy is God)
    Hi GUYS IM MR INQUISITIVE AND

    1 TIMES 2 = ...


    ... 1!!!???




    What the ****.
    Lol this. :p:
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    (Original post by im so academic)
    Lol this. :p:
    I hate typos.
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    sub in x=1 and y=7, rearrange to get C.

    voila
 
 
 
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Updated: December 27, 2010
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