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

6-72.

ASTROID

The graph of is called an "astroid."

Use implicit differentiation to find

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

Look at the derivative equation.

Now look at the graph. There are two coordinate points in which. Does the derivative exist at those points?

How about the tangent lines?Where is the derivative undefined? What happens at those points?

Look at the derivative equation. What values of

would make that equation undefined?

Now look at the graph. Describe the shape of the graph at that value of.

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*