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

8-47.

Given: *y*^{2} = *x* − *x*^{3} :

Find

. Implicit differentiation.

For what value of

*y*is there a vertical tangent to the graph?Find all

*y*-values in which the denominator of the derivative = 0.For what values of

*x*are there vertical tangents to the graph?Use the original function to find 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!)Find

. The 2nd-derivative must be written in terms of

*x*and*y*only.