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  • Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 9 maths textbook solution

Answers (1)

Answer:

f(x) is increasing on interval x \in R

Given:

f(x)=x-sin\: x

To prove:

We have to show that f(x) is increasing for all x  \in R

Hint:

Show f’(x)>0 for f(x) to be increasing.

Solution:

Given

f(x)=x-sin\: x

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(x-\sin x) \\ &\Rightarrow f^{\prime}(x)=1-\cos x \end{aligned}

Now, as given  x \in R

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

Hence condition of f(x) to be increasing.

Thus f(x) is increasing on interval x  \in R

Posted by

Gurleen Kaur

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