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Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 12

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Correct option (a)

Hint: If f(x)  is decreasing function {f}'(x)<0

Given:f(x)=\cos x-2\lambda x

Explanation: It is given that

f(x)=\cos x-2\lambda x             …….(i)

Differentiate (i) w.r.t  x

{f}'(x)=-\sin x-2\lambda

\because f(x) is decreasing {f}'(x)<0

\begin{aligned} &\therefore-\sin x-2 \lambda<0 \\ &-\sin x<2 \lambda \\ &\frac{-\sin x}{2}<\lambda \end{aligned}

\Rightarrow \frac{1}{2}<\lambda

Thus, f(x) is monotonically decreasing when \frac{1}{2}>\lambda

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