### Home > APCALC > Chapter 8 > Lesson 8.1.4 > Problem 8-47

8-47.

Given: *y*^{2} = *x* − *x*^{3} : Homework Help ✎

Write an equation for

. For what value of

*y*is there a vertical tangent to the graph?For what values of

*x*are there vertical tangents to the graph?Write an equation for

.

Implicit differentiation.

Determine all *y*-values in which the denominator of the derivative is 0.

Use the original function to determine the corresponding *x*-value for each *y*-value you found in part (b).

There will be three values of *x* that work. That means there will be three coordinate points in which the slope is vertical: ( ____, 0 ), ( ____, 0 ) and ( ____, 0 ). (Obviously, this is NOT a function!)

The second derivative must be written in terms of *x* and *y* only.