Chapter 3 - The Derivative - 3.4 Definition of the Derivative - 3.4 Exercises - Page 176: 37

$x = -3\\x = -1\\x = 0\\x = 2\\x = 3\\x = 5$

There cannot be a derivative where there is a vertical asymptote in a function. At $x = -3, x = 0$, there exists a vertical asymptote, so these points have no derivative. There cannot be a derivative where the function is not defined. At $x = 2$, the function is not defined, so this point has no derivative. There cannot be a derivative where the function takes a sharp turn. At $x = 3, x = 5$, the function takes a sharp turn, so these points have no derivative. There cannot be a derivative where the function is not continuous. At $x = -1$, the function is not continuous, so this point has no derivative.