Question

Let f(x) = |x|^1/2. Is f differentiable at c = 0?

Answer 1

Notice that for x>0,
f'(x) = 1/2 * x^(1/2-1) = 1/2 * x^(-1/2) = 1/( 2
x^(1/2) ).

Hence when x->0
lim_{x->0} f'(x) = +
infinity.

Therefore f is not differentiable at c=0 since f' in unbounded
at that point.