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

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

Answers (1)

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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