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STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
MCQ
On which of the following intervals, the function $x^{100} + sin x - 1$ is strictly increasing.
  • A
    $(0, \pi /2)$
  • B
    $(0, 1)$
  • C
    $(\pi /2, \pi )$
  • ✓
    All of the above
✓

Answer

Correct option: D.
All of the above
d
$f ' (x) = 100 x^{99} + cosx$

for $x\, \in \,(0,\,1)\,$ and $\,\left( {0\,,\,\frac{\pi }{2}} \right)\,, cosx$ and $x$ are both $+ve$ ==>$\uparrow$

for, $x\, \in \,\,\left( {\frac{\pi }{2},\;\pi } \right)\,x > 1$ hence $100 x^{99}$ obviously $> cosx $==>$\uparrow$ ]

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