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Math Help - equation of tangent #1

  1. #1
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    equation of tangent #1

    Find the equation of the tangents to the curve y=2x^2+3 that passes through the following:
    a) point (2,3)

    my work is below:
    y=2x^2+3 PP(2,3)
    y'=4x
    at x=2
    f'(2)=4(2)
    =8

    y=8x+b
    3=8(2)+b
    b=-13

    y=8x-13

    Can someone please verify or check to see if my answer or the way that i did it is correct? Thanks
    Last edited by mr fantastic; August 12th 2009 at 04:04 PM. Reason: Changed post title
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by skeske1234 View Post
    Find the equation of the tangents to the curve y=2x^2+3 that passes through the following:
    a) point (2,3)

    my work is below:
    y=2x^2+3 PP(2,3)
    y'=4x
    at x=2
    f'(2)=4(2)
    =8

    y=8x+b
    3=8(2)+b
    b=-13

    y=8x-13

    Can someone please verify or check to see if my answer or the way that i did it is correct? Thanks


    the function dose not pass through that point

    f(x)=2x^2+3 \Rightarrow f(2)=2(2)^2+3 = 8+3=11

    the function pass through (2,11) not (2,3)
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  3. #3
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    Quote Originally Posted by Amer View Post
    the function dose not pass through that point

    f(x)=2x^2+3 \Rightarrow f(2)=2(2)^2+3 = 8+3=11

    the function pass through (2,11) not (2,3)
    so what did i do wrong and how do i fix it?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by skeske1234 View Post
    so what did i do wrong and how do i fix it?
    You've done nothing wrong, you got a faulty question. Did you type it in properly?
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  5. #5
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by skeske1234 View Post
    so what did i do wrong and how do i fix it?
    the wrong is in the question not in your solution since the curve dose not pass through (2,3) so you can't find the tangent for the curve at this point but you can find the tangent at the point (2,11) since the curve pass through it
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  6. #6
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    Quote Originally Posted by e^(i*pi) View Post
    You've done nothing wrong, you got a faulty question. Did you type it in properly?
    I think it means this:
    Given the parabola y=2x^2 +3 find the equation of the tangents that passes through the point a) (2,3) and b) (2,-7)
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  7. #7
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by skeske1234 View Post
    I think it means this:
    Given the parabola y=2x^2 +3 find the equation of the tangents that passes through the point a) (2,3) and b) (2,-7)
    Yeah, it's an impossible/wrong question.

    As Amer shows in post 2 neither (2,3) nor (2,-7) lie on the line
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  8. #8
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    Quote Originally Posted by skeske1234 View Post
    Find the equation of the tangents to the curve y=2x^2+3 that passes through the following:
    a) point (2,3)
    the question asked for the lines tangent to the curve that pass thru the point (2,3) which is not on the curve.


    point on the curve ... (x, 2x^2+3)

    slope between the point on the curve and the point (2,3) ...

    m = \frac{(2x^2+3) - 3}{x - 2}

    tangent slope = 4x

    4x = \frac{2x^2}{x-2}

    4x^2 - 8x = 2x^2

    2x^2 - 8x = 0

    2x(x - 4) = 0

    x = 0 , x = 4

    point on the curve ... (0,3) , slope = 0
    the tangent line that passes through (2,3) is y = 3

    point on the curve ... (4,35), slope = 16
    the tangent line that passes through (2,3) is y = 16x - 29
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