Chapter 3.2, Problem 36E

Vertical tangent lines If a function f is continuous at a and $\underset{x\to a}{\lim }|f^{\prime }(x)|=\infty$, then the curse y = f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 31–32) is used. Use this information to answer the following questions.

36. Graph the following curves and determine the location of any vertical tangent lines.

1. a. x² + y² = 9
2. b. x² + y² + 2x = 0