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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=k x$ - $\sin x$ is strictly increasing for
  • ✓
    $k > 1$
  • B
    $k < 1$
  • C
    $k > -1$
  • D
    $k < -1$
✓

Answer

Correct option: A.
$k > 1$
Given, $f(x)=k x-\sin x$
$\Rightarrow f^{\prime}(x)=k-\cos x>0 \quad(\because f(x) \text { is strictly increasing } \therefore f(x) > 0)$
$\Rightarrow k > \cos x$
$\therefore k > 1 \quad(\because \cos x \in[-1,1])$

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