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Given: :

  1. Write an equation for .

    Implicit differentiation.

  2. For what value of is there a vertical tangent to the graph?

    Determine all -values in which the denominator of the derivative is .

  3. For what values of are there vertical tangents to the graph?

    Use the original function to determine the corresponding -value for each -value you found in part (b).

    There will be three values of that work. That means there will be three coordinate points in which the slope is vertical: ( ____, ), ( ____, ) and ( ____, ). (Obviously, this is NOT a function!)

  4. Write an equation for .

    The second derivative must be written in terms of and only.