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Math Help - Finding a tangent line

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    Finding a tangent line

    What would be the equations of the tangent lines to the graph at the following info:


    4xy+x^2=5 at the point (1,1) and (5,-1)

    If you can show me a step by step solution that would be easiest for me to follow.
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    Quote Originally Posted by AMaccy View Post
    What would be the equations of the tangent lines to the graph at the following info:


    4xy+x^2=5 at the point (1,1) and (5,-1)

    If you can show me a step by step solution that would be easiest for me to follow.
    Use "implicit differentiation" to find y': 4y+ 4xy'+ 2x= 0. 4xy'= -4y- 2x and y'= \frac{-4y-2x}{4x}

    At (1, 1), y'= \frac{-4(1)- 2(1)}{4(1)}= \frac{-6}{4}= -\frac{3}{2}. The tangent line is y= -\frac{3}{2}(x- 1)+ 1.

    At (5, -1), y'= \frac{-4(-1)- 2(5)}{4(5)}= \frac{4- 10}{20}= \frac{-6}{20}= -\frac{3}{10}. The tangent line is y= -\frac{3}{10}(x- 5)- 1.
    Last edited by mr fantastic; June 12th 2009 at 08:56 PM. Reason: Fixed a latex tag
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