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Math Help - line that is tangent to a curve ata particular point

  1. #1
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    line that is tangent to a curve ata particular point

    Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)

    I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y

    then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)

    I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?

    Thanks
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    Re: line that is tangent to a curve ata particular point

    Quote Originally Posted by Bowlbase View Post
    Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)
    I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y
    then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)
    I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?
    At the point (6,-3) we have \frac{dy}{dx}=\frac{-1}{6}.
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  3. #3
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    Re: line that is tangent to a curve ata particular point

    Really, that simple? Geez..

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    Re: line that is tangent to a curve ata particular point

    Rather than make a new thread I have similar question as before but no points given

    Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.

    I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.

    So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.

    Pretty sure this is going to be another oh geez moment. Thanks for the help.
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    Re: line that is tangent to a curve ata particular point

    Quote Originally Posted by Bowlbase View Post
    Rather than make a new thread I have similar question as before but no points given
    Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.
    I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.
    So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.
    Always, always start a new thread for a new question!

    You have two points of tangency ((1,1)~\&~(-1,-1)
    So you have two tangent lines.
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    Re: line that is tangent to a curve ata particular point

    Sorry, I'll make a new thread next time.

    So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?
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    Re: line that is tangent to a curve ata particular point

    Quote Originally Posted by Bowlbase View Post
    So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?
    since the tangent line "touches" the curve at the point of tangency, that would be correct.
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  8. #8
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    Re: line that is tangent to a curve ata particular point

    makes perfect sense, thank you.
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