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Math Help - Fun ol' Tangents

  1. #1
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    Fun ol' Tangents

    Hi,

    Could I get some help with solving this. It's probably really simple but I'm not too sure how to approach it
    ______
    'Find the equation of the tangent to the curve y=x√2x + 7 at x=3'

    Any help would be much appreciated.

    Many thanks,
    Moob
    Last edited by moob; May 2nd 2013 at 01:56 AM.
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  2. #2
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    Re: Fun ol' Tangents

    I can't read this. Is your function \displaystyle \begin{align*} y = x\,\sqrt{2}\,x^2 + 7 \end{align*} or \displaystyle \begin{align*} y = x\,\sqrt{2x^2} + 7 \end{align*} or even \displaystyle \begin{align*} y = x\,\sqrt{2x^2 + 7} \end{align*}?
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  3. #3
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    Re: Fun ol' Tangents

    Hi Prove It,

    Sorry about the misunderstanding. It should be the last one.

    Thanks a tonne!
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  4. #4
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    Re: Fun ol' Tangents

    Well the tangent line, being a line, will have equation \displaystyle \begin{align*} y = mx + c \end{align*}, so you need its gradient and its y-intercept. How will you find the gradient? How will you find the y intercept?
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  5. #5
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    Re: Fun ol' Tangents

    I've tried subbing 3 for x, this left me with
    Attachment 28224

    I am most likely way off in the method I'm using.

    Thanks once again.
    Attached Thumbnails Attached Thumbnails Fun ol' Tangents-question-4.png  
    Last edited by moob; May 2nd 2013 at 04:01 AM.
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  6. #6
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    Re: Fun ol' Tangents

    You need to find the derivative of the curve to get the gradient...
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  7. #7
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    Re: Fun ol' Tangents

    So would I replace m with this?

    Fun ol' Tangents-question-4.1.png
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  8. #8
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    Re: Fun ol' Tangents

    You would evaluated that at x = 3, and this gives you the slope, so use this along with the point (3,15) in the point-slope formula to determine the equation of the tangent line.
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  9. #9
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    Re: Fun ol' Tangents

    And no, the constant value is not 7. You will substitute x = 3, y = 15 and the value you find for m into y = mx + c and solve the equation for c.
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  10. #10
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    Re: Fun ol' Tangents

    Thank you both for all your help, I think I get it now!
    If I have any problems I'll be sure to ask.

    Thanks again!
    Last edited by moob; May 2nd 2013 at 04:27 PM.
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  11. #11
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    Re: Fun ol' Tangents

    Does this look about right to you?
    Fun ol' Tangents-question-4-final.png

    Thanks a lot!
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  12. #12
    MHF Contributor MarkFL's Avatar
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    Re: Fun ol' Tangents

    Yes, looks good to me.
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