Ex 6.2,10 - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 14, 2021 by Teachoo

Ex 6.2, 10 - Prove logarithmic function is strictly increasing

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

Transcript

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

Ex 6.2

Ex 6.2,10 You are here

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Chapter 6 Class 12 Application of Derivatives (Term 1)

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Ex 6.1
Ex 6.2
Ex 6.3
Ex 6.4
Ex 6.5
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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.