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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
Question
Is function tan x decreasing on ($0, \frac{\pi}{2}$)?
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Answer

Let f3 = tan x
$\therefore \mathrm{f}_{3}^{\prime}(\mathrm{x})=\sec ^{2} \mathrm{x}$ 
In interval $\left(0, \frac{\pi}{2}\right)$ 
$\mathrm{f}_{3}^{\prime}(\mathrm{x})=\sec ^{2} \mathrm{x}>0$ 
Therefore, f3 is strictly increasing in interval $\left(0, \frac{\pi}{2}\right)$. 

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