Example 8 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

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Example 8 Show that the function f given by f (𝑥) = 𝑥3 – 3𝑥2 + 4𝑥, 𝑥 ∈ R is strictly increasing on R. f(𝑥) = 𝑥3 – 3𝑥2 + 4𝑥 Finding f’(𝒙) f’(𝑥) = 3𝑥2 – 3.2𝑥 + 4 f’(𝑥) = 3x2 – 6𝑥 + 4 f’(𝑥) = 3x2 – 6𝑥 + 3 + 1 f’(𝑥) = 3 (𝑥2 – 2𝑥 + 1) + 1 f’(𝒙) = 3 (𝒙 – 1)2 + 1 As square is a positive number, The value of f’(𝑥) will be always positive for every real number Hence f’(𝒙) > 0 for all 𝑥 ∈ R ∴ f(𝑥) is strictly increasing

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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