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

Last updated at Jan. 7, 2020 by Teachoo

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, ∞).

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Chapter 6 Class 12 Application of Derivatives

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