Describe the x-values at which f is differentiable. (Enter your answer using interval notation.)

Question

f(x) 3x

--------

x+4

Answer 1

This function won't be differentiable at a site of non-removable discontinuity. At x = -4, where is a vertical asymptote, and both branches of this function tend towards different directions, so there is no common point that they approach from both sides (i.e., no limit), and therefore no derivative there since a derivative is a limit by definition.

Therefore, this function is differentiable on the set of x-values (-∞, -4) ∪ (-4, ∞).