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

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

Answers (1)

Answer:

 f(x) is strictly decreasing on R

Given:

f(x)=cos\: x

To prove:

We have to prove that f(x) is strictly decreasing on R.

Hint:

For f(x) to be decreasing 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(0, \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 decreasing (0, \pi).

Posted by

Gurleen Kaur

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