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Math Help - Given Derivative Thru a Point

  1. #1
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    Given Derivative Thru a Point

    Another question..

    f'(x)=1/XSQRED + 2X and goes through (-1,1).

    I need to find a function that has that derivative and passes through that point
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Super Mallow View Post
    Another question..

    f'(x)=1/XSQRED + 2X and goes through (-1,1).

    I need to find a function that has that derivative and passes through that point
    we want f(x) = \int f'(x)~dx and f(-1) = 1 as an initial condition. who do you think you should proceed?
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  3. #3
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    Hello, Super Mallow!

    f'(x)\:=\:\frac{1}{x^2} + 2x and goes through (-1,1).

    Find a function that has that derivative and passes through that point.

    We have: . f'(x) \;=\;x^{-2} + 2x

    Integrate: . f(x) \;=\;-x^{-1} + x^2 + C \;=\;-\frac{1}{x} + x^2 + C


    We are told that, when x = -1,\:f(\text{-}1) = 1

    . . So we have: . -\frac{1}{\text{-}1} + (\text{-}1)^2 + C \;=\;1\quad\Rightarrow\quad C \:=\:-1


    Therefore: . f(x)\;=\;-\frac{1}{x} + x^2 - 1

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  4. #4
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    I forgot about C =)

    That explains it, thank you!
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