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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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