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The graph of is shown below.  

  1. How many tangent lines exist at ?

    How many coordinate points does this graph have at

  2. Write the equations of the tangent lines at .

    Write two tangent line equations in point-slope form.
    You already know the points.

    Use the derivative to find the corresponding slopes. You will have to use implicit differentiation.

    Because you used implicit differentiation, your derivative might have both - and -values.
    That means you will need coordinate points to evaluate.

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 6-124 HW eTool