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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

Ex 6.2,10 Prove that the logarithmic function is strictly increasing on (0, โˆž). f(๐‘ฅ) = log (๐‘ฅ) We need to prove f(๐‘ฅ) in increasing on ๐‘ฅ โˆˆ (0 , โˆž) i.e. we need to show fโ€™ (๐‘ฅ) > 0 for x โˆˆ (0 , โˆž) Now, f(๐‘ฅ) = log ๐‘ฅ fโ€™(๐‘ฅ) = 1/๐‘ฅ When ๐‘ฅ > 0 โ‡’ (1 )/๐‘ฅ > 0 โ‡’ fโ€™(๐‘ฅ) > 0 โˆด f(๐‘ฅ) is an increasing function for ๐‘ฅ > 0 Hence, f(๐‘ฅ) is an increasing function for (0, โˆž).

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.