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Differentiability — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiability1 Mark
MCQ
Let $\text{f(x)}=|\cos\text{x}|.$ Then,
  • A
    $f(x)$ is everywhere differentiable.
  • B
    $f(x)$ is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
  • ✓
    $f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
  • D
    None of these.
✓

Answer

Correct option: C.
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
$\text{f}(\text{x)} = |\cos\text{x}|$
Given function is trigonometric function.
$\Rightarrow$ Hence, it is continuous.
Function is not differentiable at odd multiples of $\frac{\pi}{2}.$
$\Rightarrow f(x)$ is not differentiable at $\text{x} = (2\text{n} + 1) \frac{\pi}{2}$

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