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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
Let $f(x) = \left\{ \begin{array}{l}1\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\forall x < 0\\1 + \sin x,\,\,\,\forall 0 \le x \le \pi /2\end{array} \right.$, then what is the value of $f'(x)$ at $x = 0$
  • A
    $1$
  • B
    $-1$
  • C
    $\infty $
  • ✓
    does not exist
✓

Answer

Correct option: D.
does not exist
d
(d) $f(x) = \left\{ \begin{array}{l}\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\forall x < 0\\1 + \sin x ,\,\,\,\forall \,0 \le x < \frac{\pi }{2}\end{array} \right.$

$\therefore \,\,f'(x) = \left\{ \begin{array}{l}\,\,\,0,\,\,\,\,\forall \,x < 0\,({\rm{LHD}})\\\cos x,\,\,0 \le x \le \pi /2,\,\,({\rm{RHD}})\end{array} \right.$

$\therefore \,f'(0) = \left\{ \begin{array}{l}\,\,0\,\,\,\,,\,\,x < 0\\\cos 0 = 1\end{array} \right.$, 

$\therefore \,f'(0)$ does not exist.

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