### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem 6-72

6-72.

ASTROID

The graph of

*x*^{2/3}+*y*^{2/3}= 4 is called an "astroid." Homework Help ✎

Use implicit differentiation to find

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

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