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

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

Answers (1)

Answer:

f(x) = sin\: x \text { is increasing function on }(-\frac{\pi }{2},\frac{\pi }{2})

Given:

f(x) = sin\: x

To prove:

\text { We have to show that } f(x) = sin\: x \text { is increasing function on }(-\frac{\pi }{2},\frac{\pi }{2})

Hint:

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

Solution:

Given

f(x) = sin\: x

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(\sin x)\\ &\Longrightarrow f^{\prime}(x)=\cos x\\ &\text { Now, as given } x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \text { . }\\ &\Longrightarrow \cos x>0\\ &\Longrightarrow f^{\prime}(x)>0 \end{aligned}

Hence condition of f(x) to be increasing.

\text { Hence }f(x) \text { is increasing on interval }x\: \in (-\frac{\pi }{2},\frac{\pi }{2})

Posted by

Gurleen Kaur

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