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Need solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 36

Answers (1)


 b\geq 1


 f(x)=sin\: x -bx+c

To prove:

We have to find the value of b for which f(x) is decreasing function on R.


 We will apply f’(x) < 0 for decreasing then evaluate the value of b.


We have

f(x)=sin\: x -bx+c

On differentiating both sides w.r.t x we get

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(\sin x-b x+c) \\ &\Rightarrow f^{\prime}(x)=\cos x-b \end{aligned}

Given f(x) is decreasing function on R

\begin{aligned} &\Rightarrow f^{\prime}(x)<0 \text { for all } x \in R \\ &\Rightarrow \cos x-b<0 \text { for all } x \in R \\ &\Rightarrow b>\cos x \text { for all } x \in R \end{aligned}

But the least value of cos x  is 1

Hence b≥1 is required value of b.

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Gurleen Kaur

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