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Math Help - find f(x) dy/dx

  1. #1
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    find f(x) dy/dx

    The graph of y = f(x) passes through the point (1,2) and has a horizontal tangent at that point.

    If \frac{d^2y}{dx^2} = 4x - 5 find f(x) exactly.

    I have absolutely no idea on how to even approach this question

    Thank you to anyone who attempts : )
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  2. #2
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    Quote Originally Posted by qzno View Post
    The graph of y = f(x) passes through the point (1,2) and has a horizontal tangent at that point.

    If \frac{d^2y}{dx^2} = 4x - 5 find f(x) exactly.

    I have absolutely no idea on how to even approach this question

    Thank you to anyone who attempts : )
    Integrate once and set y' = 0, x = 1 to find your first constant of integration, then integrate again and use the fact that (1,2) is on the curve to find the second constant of integration.
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  3. #3
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    what do you mean by integrate and constants of integration?
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  4. #4
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    so i take the antiderivative of 4x -5 and i get 2x^2 - 5x + c and then i use the info given to solve for c?
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  5. #5
    Senior Member vincisonfire's Avatar
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    That's it. You have the conditions y(1) =2 and y'(1)=0 Don't forget to derive twice (two constants)
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