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

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

Answers (1)

Answer:

 b\geq 1

Given:

 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.

Hint:

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

Solution:

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.

Posted by

Gurleen Kaur

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