Question

If f(x) = x(√x + √(x + 1)), then

(a) f(x) is continuous but not differentiable at x = 0

(b) f(x) is differentiable at x = 0

(c) f(x) is not differentiable at x = 0

(d) None of the above

Answer 1

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.