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  • Explain solution rd sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 28

Explain solution rd sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 28

Answers (1)

Correct option (a)

Hint: Iff(x)  is increasing function{f}'(x)>0

And if f(x)  is increasing function then {f}'(x)<0

Given: f(x)=\frac{-x}{2}+\sin x

Explanation:It is given that

f(x)=\frac{-x}{2}+\sin x …..(i)

Differentiate (i) w.r.t  x

f^{\prime}(x)=\frac{-1}{2}+\cos x 

Since \because x \in\left[\frac{-\pi}{3}, \frac{\pi}{3}\right]

\begin{aligned} &\Rightarrow f^{\prime}(x)>0 \\ &\Rightarrow \frac{-1}{2}+\cos x>0 \end{aligned} 

Thus function is increasing.

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