Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.1 Introducing the Derivative - 3.1 Execises: 61

Answer

It is not differentiable at $x=2$.

Work Step by Step

The given function is a rational function and it has $x-2$ in the denominator. Since the denominator has to be different than zero we see that $x-2\neq0$ which is for $x\neq2$ and this says that $x=2$ is not in the domain of the function. Every point at which the derivative is defined (i.e. where the function is differentiable) must be in the domain. Because $x=2$ is not, the function is not differentiable at $x=2$.
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