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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x+\sin x$ is
  • ✓
    always increasing
  • B
    always decreasing
  • C
    increasing for certain range of $x$
  • D
    None of these
✓

Answer

Correct option: A.
always increasing
(a) : $\because f(x)=x+\sin x$
Differentiating w.r.t. $x$, we get $f^{\prime}(x)=1+\cos x$
$f^{\prime}(x) \geq 0$ for all values of $x$
$(\because \cos x$ is lying between -1 to 1 )
$\therefore f(x)$ is always increasing.

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