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

The graph of is called an astroid. 6-72 HW eTool (Desmos). Homework Help ✎

Use implicit differentiation to find

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

Look at the derivative equation. Will values of

*y*or values of*x*make the derivative 0?A horizontal tangent should exist when

, which happens when . 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

*x*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.

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