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Example 7 - Show that f(x) = 7x - 3 is strictly increasing

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Example 7 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Example 7 (Method 1) Show that the function given by f (π‘₯) = 7π‘₯ – 3 is strictly increasing on R.f(π‘₯) = 7π‘₯ – 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 π‘₯1 and π‘₯2 be real numbers Such that π’™πŸ < 𝒙2 Multiplying both sides by 7 7π‘₯1 < 7π‘₯2 Subtracting both sides by 3 7π‘₯1 βˆ’ 3 < 7π‘₯2 βˆ’ 3 f (π’™πŸ) < 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.