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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives2 Marks
Question
Prove that the logarithmic function is increasing on $(0, \infty)$.
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Answer

The given function is f(x) = log x
$\Rightarrow$ f'(x) = $\frac{1}{x}$,.
Clearly, for x > 0,
     f'(x) = $\frac{1}{x}$ > 0
Therefore, f(x) = log x is strictly increasing in interval $(0, \infty)$

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