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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
Question
Prove that the logarithmic function is strictly increasing on $(0,\infty).$
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Answer

Given: $\text{f}\text{(x)} = \log \text{x}\ \Rightarrow\ \text{f}'\text{(x)} = \frac{1}{\text{x}} \text{for all x}\text{ in} (0,\ \infty).$
Therefore, f(x) is strictly increasing on $(0,\ \infty).$

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