The graph of x2/3 + y2/3 = 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.
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