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  • Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 37 maths

Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 37 maths

Answers (1)

Answer:

 f(x) is an increasing function on R or all the value of a

Given:

 f(x)=x+cos\: x -a

To prove:

We have to show that f(x) is an increasing function on R or all the value of a.

Hint:

For f(x) to be increasing function we must have f’(x) > 0.

Solution:

Here we have

f(x)=x+cos\: x -a

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(x+\cos x-a) \\ &\Rightarrow f^{\prime}(x)=1-\sin x,\left[\frac{d}{d x}(\text { constant })=0\right] \\ &\text { Since }-1 \leq \sin x \leq 1 \end{aligned}

Then we have,

\begin{aligned} &1-\sin x \geq 0 \text { for all value of } x\\ &\operatorname{So}f^{\prime}(x) \geq 0 \text { forall } x \in R \end{aligned}

Hence the function is increasing on Rf or all value of a.

Posted by

Gurleen Kaur

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