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

8-47.

Given: :

Write an equation for

. Implicit differentiation.

For what value of

is there a vertical tangent to the graph?Determine all

-values in which the denominator of the derivative is. For what values of

are there vertical tangents to the graph?Use the original function to determine the corresponding

-value for each-value you found in part (b).There will be three values of

that work. That means there will be three coordinate points in which the slope is vertical: ( ____,), ( ____, ) and ( ____, ). (Obviously, this is NOT a function!) Write an equation for

. The second derivative must be written in terms of

andonly.