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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
Let $f(x)=|x|$ and $g(x)=\left|x^3\right|,$ then :
  • ✓
    $f(x)$ and $g(x)$ both are continuous at $x = 0$
  • B
    $f(x$) and $g(x)$ both are differentiable at $x = 0$
  • C
    $f(x)$ is differentiable but $g(x)$ is not differentiable at $x = 0$
  • D
    $f(x)$ and $g(x)$ both are not differentiable at $x = 0$
✓

Answer

Correct option: A.
$f(x)$ and $g(x)$ both are continuous at $x = 0$
Absolute value function is continuous on $R.$

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