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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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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