the function f is not differentiable at x=5 which of the following must be true

Question

the function f is not differentiable at x=5 which of the following must be true

f is not continuous at x=5

limit as x approaches 5 f(x) does not exist

lim as x approaches 5 (f(x)-f(5))/(x-5) does not exist

lim upper =5 lower =0 f(x) dx does not exist

Answer 1

The definition of derivative at x=5 is

f'(5) = lim as x approaches 5 (f(x)-f(5))/(x-5)

Therefore "not differentiable" means that the limit does not exist.