Example 7 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

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Example 7 (Method 1) Show that the function given by f (𝑥) = 7𝑥 – 3 is strictly increasing on R.f(𝑥) = 7𝑥 – 3 Finding f’(𝒙) f’(x) = (7x – 3)’ f’(x) = 7 Since f’(𝒙) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x – 3 is strictly increasing on R. Let 𝑥1 and 𝑥2 be real numbers Such that 𝒙𝟏 < 𝒙2 Multiplying both sides by 7 7𝑥1 < 7𝑥2 Subtracting both sides by 3 7𝑥1 − 3 < 7𝑥2 − 3 f (𝒙𝟏) < f ( 𝒙2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.

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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 and Computer Science at Teachoo