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.
Graph the following functions and determine the location of the vertical tangent lines.
a. f(x) = (x − 2)1/3
b. f(x) = (x + 1)2/3
c.
d. f(x) = x5/3 – 2x1/3
Exercises 1
f(x) = |x − 2|; a = 2
Exercises 2
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