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Math Help - Primitive Functions

  1. #1
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    Exclamation Primitive Functions

    At all points on a certan curve, y'' = 2x. The point (3,6) belongs to the curve and its tangent at this point is inclined at 45 degrees to the X-axis. Find the equation of the curve.

    How exactly do I use the bold part for this problem? I've found y' = x^2 + c...

    Oh, and is the answer actually y = x^2 - 5x + 12 (txtbk answer) cause it doesn't look right to me.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by xwrathbringerx View Post
    At all points on a certan curve, y'' = 2x. The point (3,6) belongs to the curve and its tangent at this point is inclined at 45 degrees to the X-axis. Find the equation of the curve.

    How exactly do I use the bold part for this problem? I've found y' = x^2 + c...

    Oh, and is the answer actually y = x^2 - 5x + 12 (txtbk answer) cause it doesn't look right to me.
    The bolded part informs you that y^{\prime}(3)=1.

    So this is a differential equation y^{\prime\prime}=2x with y(3)=6 and y^{\prime}(3)=1

    I'm sure you can proceed from here.
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