Chapter 3 - The Derivative - 3.4 Definition of the Derivative - 3.4 Exercises - Page 176: 38

$x = -5\\x = -3\\x = 2\\x = 0\\x = 4$

There can be no derivative where there is a vertical asymptote. At $x = -5$, there is a vertical asymptote, so this point has no derivative. There can be no derivative where the function takes sharp turns. At $x = -3, x = 2$, the function takes sharp turns, so these points have no derivative. There can be no derivative where the function is not defined. At $x = 0$, the function is not defined, so this point has no derivative. There can be no derivative where the tangential line of a function at a given point is completely vertical. At $x = 4$, the tangential line of the function at the given point is completely vertical, so this point has no derivative.