Question

The function f(x) = |x| V x ∈ R is

A. continuous but not differentiable at x = 0

B. differentiable but not continuous at x = 0

C. neither continuous nor differentiable at x = 0

D. none of these

Answer 1

(Sometimes it’s easier to get the answer by graphs)

Now in the above graph

We can see f(x) is Continuous on 0.

But it has sharp curve on x = 0 which implies it is not differentiable.