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  • Need solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 33 subquestion (ii)

Need solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 33 subquestion (ii)

Answers (1)

Answer:

f(x) is strictly increasing in (\pi,2\pi)

Given:

f(x)=cos\: x

To prove:

We have to prove that f(x) is strictly increasing in (\pi,2\pi)

Hint:

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

Solution:

Given

f(x)=cos\: x

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(\cos x)\\ &\Rightarrow f^{\prime}(x)=-\sin x\\ &\text { Since for each } x \in(\pi, 2 \pi), \sin x<0\\ &\Rightarrow-\sin x>0 \end{aligned}

By applying negative sign change comparison sign.

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

Hence f(x) is strictly increasing on (\pi,2\pi)

Posted by

Gurleen Kaur

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