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  • Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 14

Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 14

Answers (1)

Answer:

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

Given:

f(x) =tan \: x

To prove:

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

Hint:

Condition for increasing function f’(x)>0.

Solution:

Given

f(x) =tan \: x

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

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(\tan x)\\ &\Rightarrow f^{\prime}(x)=\sec ^{2} x\\ \end{aligned}

Now, as given

\begin{aligned} &x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \end{aligned}

i.e, 4th quadrant to 1st quadrant, where

\begin{aligned} \Rightarrow sec^{2}\: x> 0 \\ \Rightarrow f'(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}).

Hence proved.

Posted by

Gurleen Kaur

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