If f(x) = x( x - x + 1 ), then - Vidyadip

MCQ

If $f(x) = x(\sqrt x - \sqrt {x + 1} ),$ then

A
$f(x)$ is continuous but non- differentiable at $x = 0$
B
$f(x)$ is differentiable at $x = 0$
✓
$f(x)$ is not differentiable at $x = 0$
D
None of these

✓

Answer

Correct option: C.

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

c
(c) Since the function is defined for $x \ge 0$ $i.e.$ not defined for $x < 0$.

Hence the function neither continuous nor differentiable at $x = 0$.

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