Vertical tangent lines If a function f is continuous at a and , then the curve y = f(x) ha...

Vertical tangent lines If a function f is continuous at a and , then the curve 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 1–2) is used. Use this information to answer the following question.

The preceding definition of a vertical tangent line includes four cases:  combined with

(for example, one case is .

Sketch a continuous function that has a vertical tangent line at a in each of the four cases.

Exercises 1

f(x) = |x − 2|; a = 2

Exercises 2