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6-72.
  1. ASTROID

  2. The graph of x2/3 + y2/3 = 4 is called an "astroid." Homework Help ✎

    1. Use implicit differentiation to find .

    2. Where does the astroid have a horizontal tangent? Explain.

    3. Where is the derivative undefined? What happens at those points?

Look at the derivative equation.

Now look at the graph. There are two coordinate points in which y = 0. Does the derivative exist at those points?
How about the tangent lines?

Look at the derivative equation. What values of x would make that equation undefined?
Now look at the graph. Describe the shape of the graph at that value of x.

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 6-72 HW eTool