Correct option (c) f(x) is not differentiable at x = 0
Explanation :
f(x) = x(√x + √(x + 1)),
f(x)would exists when x ≥ 0 and x + 1 ≥ 0
f(x) would exists when x ≥ 0.
f(x) is not continuous at x = 0, because LHL does not exist.
Hence, option (c) is correct.