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Ex 6.2, 10 - Prove logarithmic function is strictly increasing

Ex 6.2,10 - Chapter 6 Class 12 Application of Derivatives - Part 2


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Ex 6.2, 10 Prove that the logarithmic function is strictly increasing on (0, ∞).f(𝑥) = log (𝑥) We need to prove f(𝑥) in increasing on 𝑥 ∈ (0 , ∞) i.e. we need to show f’(𝒙) > 0 for x ∈ (𝟎 , ∞) Now, f(𝑥) = log 𝑥 f’(𝑥) = 1/𝑥 When 𝒙 > 0 (1 )/𝑥 > 0 f’(𝑥) > 0 ∴ f(𝑥) is an increasing function for 𝑥 > 0 Hence, f(𝑥) is an increasing function for (0, ∞). Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.